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Author: Charles B. Thomas
Publisher: Springer Science & Business Media
ISBN: 0306469693
Category : Mathematics
Languages : en
Pages : 202
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Book Description
Elliptic cohomology is an extremely beautiful theory with both geometric and arithmetic aspects. The former is explained by the fact that the theory is a quotient of oriented cobordism localised away from 2, the latter by the fact that the coefficients coincide with a ring of modular forms. The aim of the book is to construct this cohomology theory, and evaluate it on classifying spaces BG of finite groups G. This class of spaces is important, since (using ideas borrowed from `Monstrous Moonshine') it is possible to give a bundle-theoretic definition of EU-(BG). Concluding chapters also discuss variants, generalisations and potential applications.
Author: Charles B. Thomas
Publisher: Springer Science & Business Media
ISBN: 0306469693
Category : Mathematics
Languages : en
Pages : 202
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Book Description
Elliptic cohomology is an extremely beautiful theory with both geometric and arithmetic aspects. The former is explained by the fact that the theory is a quotient of oriented cobordism localised away from 2, the latter by the fact that the coefficients coincide with a ring of modular forms. The aim of the book is to construct this cohomology theory, and evaluate it on classifying spaces BG of finite groups G. This class of spaces is important, since (using ideas borrowed from `Monstrous Moonshine') it is possible to give a bundle-theoretic definition of EU-(BG). Concluding chapters also discuss variants, generalisations and potential applications.
Author: Haynes R. Miller
Publisher: Cambridge University Press
ISBN: 052170040X
Category : Mathematics
Languages : en
Pages : 17
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Book Description
First collection of papers on elliptic cohomology in twenty years; represents the diversity of topics within this important field.
Author: Joseph H. Silverman
Publisher: Springer Science & Business Media
ISBN: 1475742525
Category : Mathematics
Languages : en
Pages : 292
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Book Description
The theory of elliptic curves involves a blend of algebra, geometry, analysis, and number theory. This book stresses this interplay as it develops the basic theory, providing an opportunity for readers to appreciate the unity of modern mathematics. The book’s accessibility, the informal writing style, and a wealth of exercises make it an ideal introduction for those interested in learning about Diophantine equations and arithmetic geometry.
Author: Stefan Schwede
Publisher: Cambridge University Press
ISBN: 110842581X
Category : Mathematics
Languages : en
Pages : 847
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Book Description
A comprehensive, self-contained approach to global equivariant homotopy theory, with many detailed examples and sample calculations.
Author: Nils Baas
Publisher: Springer Science & Business Media
ISBN: 3642012000
Category : Mathematics
Languages : en
Pages : 417
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Book Description
The 2007 Abel Symposium took place at the University of Oslo in August 2007. The goal of the symposium was to bring together mathematicians whose research efforts have led to recent advances in algebraic geometry, algebraic K-theory, algebraic topology, and mathematical physics. A common theme of this symposium was the development of new perspectives and new constructions with a categorical flavor. As the lectures at the symposium and the papers of this volume demonstrate, these perspectives and constructions have enabled a broadening of vistas, a synergy between once-differentiated subjects, and solutions to mathematical problems both old and new.
Author: Daniel G. Davis
Publisher: American Mathematical Soc.
ISBN: 1470442442
Category : Literary Collections
Languages : en
Pages : 282
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Book Description
This volume contains the proceedings of the conference Homotopy Theory: Tools and Applications, in honor of Paul Goerss's 60th birthday, held from July 17–21, 2017, at the University of Illinois at Urbana-Champaign, Urbana, IL. The articles cover a variety of topics spanning the current research frontier of homotopy theory. This includes articles concerning both computations and the formal theory of chromatic homotopy, different aspects of equivariant homotopy theory and K-theory, as well as articles concerned with structured ring spectra, cyclotomic spectra associated to perfectoid fields, and the theory of higher homotopy operations.
Author: Robert S. Doran
Publisher: American Mathematical Soc.
ISBN: 0821848879
Category : Mathematics
Languages : en
Pages : 265
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Book Description
This volume contains the proceedings of an NSF-CBMS Conference held at Texas Christian University in Fort Worth, Texas, May 18-22, 2009. The papers, written especially for this volume by well-known mathematicians and mathematical physicists, are an outgrowth of the talks presented at the conference. Topics examined are highly interdisciplinary and include, among many other things, recent results on D-brane charges in $K$-homology and twisted $K$-homology, Yang-Mills gauge theory and connections with non-commutative geometry, Landau-Ginzburg models, $C^*$-algebraic non-commutative geometry and ties to quantum physics and topology, the rational homotopy type of the group of unitary elements in an Azumaya algebra, and functoriality properties in the theory of $C^*$-crossed products and fixed point algebras for proper actions. An introduction, written by Jonathan Rosenberg, provides an instructive overview describing common themes and how the various papers in the volume are interrelated and fit together. The rich diversity of papers appearing in the volume demonstrates the current interplay between superstring theory, geometry/topology, and non-commutative geometry. The book will be of interest to graduate students, mathematicians, mathematical physicists, and researchers working in these areas.
Author: Nicholas Kuhn
Publisher: American Mathematical Soc.
ISBN: 0821826212
Category : Mathematics
Languages : en
Pages : 370
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Book Description
This volume presents the proceedings from the AMS-IMS-SIAM Summer Research Conference on Homotopy Methods in Algebraic Topology held at the University of Colorado (Boulder). The conference coincided with the sixtieth birthday of J. Peter May. An article is included reflecting his wide-ranging and influential contributions to the subject area. Other articles in the book discuss the ordinary, elliptic and real-oriented Adams spectral sequences, mapping class groups, configuration spaces, extended powers, operads, the telescope conjecture, $p$-compact groups, algebraic K theory, stable and unstable splittings, the calculus of functors, the $E_{\infty}$ tensor product, and equivariant cohomology theories. The book offers a compendious source on modern aspects of homotopy theoretic methods in many algebraic settings.
Author: John P. Harnad
Publisher: American Mathematical Soc.
ISBN: 0821870424
Category : Mathematics
Languages : en
Pages : 387
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Book Description
Author: Haynes Miller
Publisher: CRC Press
ISBN: 1351251619
Category : Mathematics
Languages : en
Pages : 982
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Book Description
The Handbook of Homotopy Theory provides a panoramic view of an active area in mathematics that is currently seeing dramatic solutions to long-standing open problems, and is proving itself of increasing importance across many other mathematical disciplines. The origins of the subject date back to work of Henri Poincaré and Heinz Hopf in the early 20th century, but it has seen enormous progress in the 21st century. A highlight of this volume is an introduction to and diverse applications of the newly established foundational theory of ¥ -categories. The coverage is vast, ranging from axiomatic to applied, from foundational to computational, and includes surveys of applications both geometric and algebraic. The contributors are among the most active and creative researchers in the field. The 22 chapters by 31 contributors are designed to address novices, as well as established mathematicians, interested in learning the state of the art in this field, whose methods are of increasing importance in many other areas.
