Author: John Patrick Campbell Greenlees
Publisher: American Mathematical Soc.
ISBN: 0821826034
Category : Mathematics
Languages : en
Pages : 193
Book Description
Let [italic capital]G be a compact Lie group, [italic capitals]EG a contractible free [italic capital]G-space and let [italic capitals]E~G be the unreduced suspension of [italic capitals]EG with one of the cone points as basepoint. Let [italic]k*[over][subscript italic capital]G be a [italic capital]G-spectrum. Let [italic capital]X+ denote the disjoint union of [italic capital]X and a [italic capital]G-fixed basepoint. Define the [italic capital]G-spectra [italic]f([italic]k*[over][subscript italic capital]G) = [italic]k*[over][subscript italic capital]G [up arrowhead symbol] [italic capitals]EG+, [italic]c([italic]k*[over][subscript italic capital]G) = [italic capital]F([italic capitals]EG+,[italic]k*[over][subscript italic capital]G), and [italic]t([italic]k[subscript italic capital]G)* = [italic capital]F([italic capitals]EG+,[italic]k*[over][subscript italic capital]G) [up arrowhead symbol] [italic capitals]E~G. The last of these is the [italic capital]G-spectrum representing the generalized Tate homology and cohomology theories associated to [italic]k[subscript italic capital]G. Here [italic capital]F([italic capitals]EG+,[italic]k*[over][subscript italic capital]G) is the function space spectrum. The authors develop the properties of these theories, illustrating the manner in which they generalize the classical Tate-Swan theories.
Generalized Tate Cohomology
Author: John Patrick Campbell Greenlees
Publisher: American Mathematical Soc.
ISBN: 0821826034
Category : Mathematics
Languages : en
Pages : 193
Book Description
Let [italic capital]G be a compact Lie group, [italic capitals]EG a contractible free [italic capital]G-space and let [italic capitals]E~G be the unreduced suspension of [italic capitals]EG with one of the cone points as basepoint. Let [italic]k*[over][subscript italic capital]G be a [italic capital]G-spectrum. Let [italic capital]X+ denote the disjoint union of [italic capital]X and a [italic capital]G-fixed basepoint. Define the [italic capital]G-spectra [italic]f([italic]k*[over][subscript italic capital]G) = [italic]k*[over][subscript italic capital]G [up arrowhead symbol] [italic capitals]EG+, [italic]c([italic]k*[over][subscript italic capital]G) = [italic capital]F([italic capitals]EG+,[italic]k*[over][subscript italic capital]G), and [italic]t([italic]k[subscript italic capital]G)* = [italic capital]F([italic capitals]EG+,[italic]k*[over][subscript italic capital]G) [up arrowhead symbol] [italic capitals]E~G. The last of these is the [italic capital]G-spectrum representing the generalized Tate homology and cohomology theories associated to [italic]k[subscript italic capital]G. Here [italic capital]F([italic capitals]EG+,[italic]k*[over][subscript italic capital]G) is the function space spectrum. The authors develop the properties of these theories, illustrating the manner in which they generalize the classical Tate-Swan theories.
Publisher: American Mathematical Soc.
ISBN: 0821826034
Category : Mathematics
Languages : en
Pages : 193
Book Description
Let [italic capital]G be a compact Lie group, [italic capitals]EG a contractible free [italic capital]G-space and let [italic capitals]E~G be the unreduced suspension of [italic capitals]EG with one of the cone points as basepoint. Let [italic]k*[over][subscript italic capital]G be a [italic capital]G-spectrum. Let [italic capital]X+ denote the disjoint union of [italic capital]X and a [italic capital]G-fixed basepoint. Define the [italic capital]G-spectra [italic]f([italic]k*[over][subscript italic capital]G) = [italic]k*[over][subscript italic capital]G [up arrowhead symbol] [italic capitals]EG+, [italic]c([italic]k*[over][subscript italic capital]G) = [italic capital]F([italic capitals]EG+,[italic]k*[over][subscript italic capital]G), and [italic]t([italic]k[subscript italic capital]G)* = [italic capital]F([italic capitals]EG+,[italic]k*[over][subscript italic capital]G) [up arrowhead symbol] [italic capitals]E~G. The last of these is the [italic capital]G-spectrum representing the generalized Tate homology and cohomology theories associated to [italic]k[subscript italic capital]G. Here [italic capital]F([italic capitals]EG+,[italic]k*[over][subscript italic capital]G) is the function space spectrum. The authors develop the properties of these theories, illustrating the manner in which they generalize the classical Tate-Swan theories.
Generalized Tate Cohomology
Author: Alina Claudia Iacob
Publisher:
ISBN:
Category :
Languages : en
Pages : 88
Book Description
Publisher:
ISBN:
Category :
Languages : en
Pages : 88
Book Description
Equivariant Homotopy and Cohomology Theory
Author: J. Peter May
Publisher: American Mathematical Soc.
ISBN: 0821803190
Category : Mathematics
Languages : en
Pages : 384
Book Description
This volume introduces equivariant homotopy, homology, and cohomology theory, along with various related topics in modern algebraic topology. It explains the main ideas behind some of the most striking recent advances in the subject. The works begins with a development of the equivariant algebraic topology of spaces culminating in a discussion of the Sullivan conjecture that emphasizes its relationship with classical Smith theory. The book then introduces equivariant stable homotopy theory, the equivariant stable homotopy category, and the most important examples of equivariant cohomology theories. The basic machinery that is needed to make serious use of equivariant stable homotopy theory is presented next, along with discussions of the Segal conjecture and generalized Tate cohomology. Finally, the book gives an introduction to "brave new algebra", the study of point-set level algebraic structures on spectra and its equivariant applications. Emphasis is placed on equivariant complex cobordism, and related results on that topic are presented in detail.
Publisher: American Mathematical Soc.
ISBN: 0821803190
Category : Mathematics
Languages : en
Pages : 384
Book Description
This volume introduces equivariant homotopy, homology, and cohomology theory, along with various related topics in modern algebraic topology. It explains the main ideas behind some of the most striking recent advances in the subject. The works begins with a development of the equivariant algebraic topology of spaces culminating in a discussion of the Sullivan conjecture that emphasizes its relationship with classical Smith theory. The book then introduces equivariant stable homotopy theory, the equivariant stable homotopy category, and the most important examples of equivariant cohomology theories. The basic machinery that is needed to make serious use of equivariant stable homotopy theory is presented next, along with discussions of the Segal conjecture and generalized Tate cohomology. Finally, the book gives an introduction to "brave new algebra", the study of point-set level algebraic structures on spectra and its equivariant applications. Emphasis is placed on equivariant complex cobordism, and related results on that topic are presented in detail.
Generalized Cohomology
Author: Akira Kōno
Publisher: American Mathematical Soc.
ISBN: 9780821835142
Category : Mathematics
Languages : en
Pages : 276
Book Description
Aims to give an exposition of generalized (co)homology theories that can be read by a group of mathematicians who are not experts in algebraic topology. This title starts with basic notions of homotopy theory, and introduces the axioms of generalized (co)homology theory. It also discusses various types of generalized cohomology theories.
Publisher: American Mathematical Soc.
ISBN: 9780821835142
Category : Mathematics
Languages : en
Pages : 276
Book Description
Aims to give an exposition of generalized (co)homology theories that can be read by a group of mathematicians who are not experts in algebraic topology. This title starts with basic notions of homotopy theory, and introduces the axioms of generalized (co)homology theory. It also discusses various types of generalized cohomology theories.
Equivariant Homotopy and Cohomology Theory
Author: M. Cole
Publisher: American Mathematical Soc.
ISBN: 0821889354
Category : Science
Languages : en
Pages : 384
Book Description
This volume introduces equivariant homotopy, homology, and cohomology theory, along with various related topics in modern algebraic topology. It explains the main ideas behind some of the most striking recent advances in the subject. The works begins with a development of the equivariant algebraic topology of spaces culminating in a discussion of the Sullivan conjecture that emphasizes its relationship with classical Smith theory. The book then introduces equivariant stable homotopy theory, the equivariant stable homotopy category, and the most important examples of equivariant cohomology theories. The basic machinery that is needed to make serious use of equivariant stable homotopy theory is presented next, along with discussions of the Segal conjecture and generalized Tate cohomology. Finally, the book gives an introduction to "brave new algebra", the study of point-set level algebraic structures on spectra and its equivariant applications. Emphasis is placed on equivariant complex cobordism, and related results on that topic are presented in detail.
Publisher: American Mathematical Soc.
ISBN: 0821889354
Category : Science
Languages : en
Pages : 384
Book Description
This volume introduces equivariant homotopy, homology, and cohomology theory, along with various related topics in modern algebraic topology. It explains the main ideas behind some of the most striking recent advances in the subject. The works begins with a development of the equivariant algebraic topology of spaces culminating in a discussion of the Sullivan conjecture that emphasizes its relationship with classical Smith theory. The book then introduces equivariant stable homotopy theory, the equivariant stable homotopy category, and the most important examples of equivariant cohomology theories. The basic machinery that is needed to make serious use of equivariant stable homotopy theory is presented next, along with discussions of the Segal conjecture and generalized Tate cohomology. Finally, the book gives an introduction to "brave new algebra", the study of point-set level algebraic structures on spectra and its equivariant applications. Emphasis is placed on equivariant complex cobordism, and related results on that topic are presented in detail.
Gorenstein Homological Algebra
Author: Alina Iacob
Publisher: CRC Press
ISBN: 1351660268
Category : Mathematics
Languages : en
Pages : 214
Book Description
Gorenstein homological algebra is an important area of mathematics, with applications in commutative and noncommutative algebra, model category theory, representation theory, and algebraic geometry. While in classical homological algebra the existence of the projective, injective, and flat resolutions over arbitrary rings are well known, things are a little different when it comes to Gorenstein homological algebra. The main open problems in this area deal with the existence of the Gorenstein injective, Gorenstein projective, and Gorenstein flat resolutions. Gorenstein Homological Algebra is especially suitable for graduate students interested in homological algebra and its applications.
Publisher: CRC Press
ISBN: 1351660268
Category : Mathematics
Languages : en
Pages : 214
Book Description
Gorenstein homological algebra is an important area of mathematics, with applications in commutative and noncommutative algebra, model category theory, representation theory, and algebraic geometry. While in classical homological algebra the existence of the projective, injective, and flat resolutions over arbitrary rings are well known, things are a little different when it comes to Gorenstein homological algebra. The main open problems in this area deal with the existence of the Gorenstein injective, Gorenstein projective, and Gorenstein flat resolutions. Gorenstein Homological Algebra is especially suitable for graduate students interested in homological algebra and its applications.
Computational and Geometric Aspects of Modern Algebra
Author: Michael D. Atkinson
Publisher: Cambridge University Press
ISBN: 9780521788892
Category : Mathematics
Languages : en
Pages : 290
Book Description
A collection of papers from leading researchers in algebra and geometric group theory.
Publisher: Cambridge University Press
ISBN: 9780521788892
Category : Mathematics
Languages : en
Pages : 290
Book Description
A collection of papers from leading researchers in algebra and geometric group theory.
Abelian Groups, Rings, Modules, and Homological Algebra
Author: Pat Goeters
Publisher: CRC Press
ISBN: 142001076X
Category : Mathematics
Languages : en
Pages : 354
Book Description
About the book In honor of Edgar Enochs and his venerable contributions to a broad range of topics in Algebra, top researchers from around the world gathered at Auburn University to report on their latest work and exchange ideas on some of today's foremost research topics. This carefully edited volume presents the refereed papers of the par
Publisher: CRC Press
ISBN: 142001076X
Category : Mathematics
Languages : en
Pages : 354
Book Description
About the book In honor of Edgar Enochs and his venerable contributions to a broad range of topics in Algebra, top researchers from around the world gathered at Auburn University to report on their latest work and exchange ideas on some of today's foremost research topics. This carefully edited volume presents the refereed papers of the par
Geometric and Cohomological Methods in Group Theory
Author: Martin R. Bridson
Publisher: Cambridge University Press
ISBN: 052175724X
Category : Mathematics
Languages : en
Pages : 331
Book Description
An extended tour through a selection of the most important trends in modern geometric group theory.
Publisher: Cambridge University Press
ISBN: 052175724X
Category : Mathematics
Languages : en
Pages : 331
Book Description
An extended tour through a selection of the most important trends in modern geometric group theory.
Combinatorial and Geometric Group Theory, Edinburgh 1993
Author: Andrew J. Duncan
Publisher: Cambridge University Press
ISBN: 9780521465953
Category : Mathematics
Languages : en
Pages : 340
Book Description
Authoritative collection of surveys and papers that will be indispensable to all research workers in the area.
Publisher: Cambridge University Press
ISBN: 9780521465953
Category : Mathematics
Languages : en
Pages : 340
Book Description
Authoritative collection of surveys and papers that will be indispensable to all research workers in the area.