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Author: Milé Krajčevski
Publisher: American Mathematical Soc.
ISBN: 0821827626
Category : Mathematics
Languages : en
Pages : 74
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Book Description
This book is intended for graduate students and research mathematicians interested in group theory and generalizations.
Author: Milé Krajčevski
Publisher: American Mathematical Soc.
ISBN: 0821827626
Category : Mathematics
Languages : en
Pages : 74
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Book Description
This book is intended for graduate students and research mathematicians interested in group theory and generalizations.
Author: José Ignacio Cogolludo-Agustín
Publisher: American Mathematical Soc.
ISBN: 0821829424
Category : Mathematics
Languages : en
Pages : 97
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Book Description
The authors analyse two topological invariants of an embedding of an arrangement of rational plane curves in the projective complex plane, namely, the cohomology ring of the complement and the characteristic varieties. Their main result states that the cohomology ring of the complement to a rational arrangement is generated by logarithmic 1 and 2-forms and its structure depends on a finite number of invariants of the curve (its combinatorial type).
Author: Robert Bieri
Publisher: American Mathematical Soc.
ISBN: 0821831844
Category : Mathematics
Languages : en
Pages : 105
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Book Description
Generalizing the Bieri-Neumann-Strebel-Renz Invariants, this Memoir presents the foundations of a theory of (not necessarily discrete) actions $\rho$ of a (suitable) group $G$ by isometries on a proper CAT(0) space $M$. The passage from groups $G$ to group actions $\rho$ implies the introduction of 'Sigma invariants' $\Sigmak(\rho)$ to replace the previous $\Sigmak(G)$ introduced by those authors. Their theory is now seen as a special case of what is studied here so that readers seeking a detailed treatment of their theory will find it included here as a special case. We define and study 'controlled $k$-connectedness $(CCk)$' of $\rho$, both over $M$ and over end points $e$ in the 'boundary at infinity' $\partial M$; $\Sigmak(\rho)$ is by definition the set of all $e$ over which the action is $(k-1)$-connected. A central theorem, the Boundary Criterion, says that $\Sigmak(\rho) = \partial M$ if and only if $\rho$ is $CC{k-1}$ over $M$.An Openness Theorem says that $CCk$ over $M$ is an open condition on the space of isometric actions $\rho$ of $G$ on $M$. Another Openness Theorem says that $\Sigmak(\rho)$ is an open subset of $\partial M$ with respect to the Tits metric topology. When $\rho(G)$ is a discrete group of isometries the property $CC{k-1}$ is equivalent to ker$(\rho)$ having the topological finiteness property type '$F_k$'. More generally, if the orbits of the action are discrete, $CC{k-1}$ is equivalent to the point-stabilizers having type $F_k$. In particular, for $k=2$ we are characterizing finite presentability of kernels and stabilizers. Examples discussed include: locally rigid actions, translation actions on vector spaces (especially those by metabelian groups
Author: Donald M. Davis
Publisher: American Mathematical Soc.
ISBN: 0821829874
Category : Mathematics
Languages : en
Pages : 65
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Book Description
A formula for the odd-primary v1-periodic homotopy groups of a finite H-space in terms of its K-theory and Adams operations has been obtained by Bousfield. This work applys this theorem to give explicit determinations of the v1-periodic homotopy groups of (E8,5) and (E8,3), thus completing the determination of all odd-primary v1-periodic homotopy groups of all compact simple Lie groups, a project suggested by Mimura in 1989.
Author: Armand Borel
Publisher: American Mathematical Soc.
ISBN: 0821827928
Category : Mathematics
Languages : en
Pages : 153
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Book Description
This text describes the components of the moduli space of conjugacy classes of commuting pairs and triples of elements in a compact Lie group. This description is in the extended Dynkin diagram of the simply connected cover, together with the co-root integers and the action of the fundamental group. In the case of three commuting elements, we compute Chern-Simons invariants associated to the corresponding flat bundles over the three-torus, and verify a conjecture of Witten which reveals a surprising symmetry involving the Chern-Simons invariants and the dimensions of the components of the moduli space.
Author: Robert Ray Bruner
Publisher: American Mathematical Soc.
ISBN: 0821833669
Category : Mathematics
Languages : en
Pages : 144
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Book Description
Includes a paper that deals the connective K homology and cohomology of finite groups $G$. This title uses the methods of algebraic geometry to study the ring $ku DEGREES*(BG)$ where $ku$ denotes connective complex K-theory. It describes the variety in terms of the category of abelian $p$-subgroups of $G$ for primes $p$ dividing the group
Author: Nanhua Xi
Publisher: American Mathematical Soc.
ISBN: 0821828916
Category : Mathematics
Languages : en
Pages : 114
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Book Description
In this paper we prove Lusztig's conjecture on based ring for an affine Weyl group of type $\tilde A_{n-1}$.
Author: L. Rodman
Publisher: American Mathematical Soc.
ISBN: 0821829963
Category : Mathematics
Languages : en
Pages : 87
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Book Description
In this work, versions of an abstract scheme are developed, which are designed to provide a framework for solving a variety of extension problems. The abstract scheme is commonly known as the band method. The main feature of the new versions is that they express directly the conditions for existence of positive band extensions in terms of abstract factorizations (with certain additional properties). The results prove, amongst other things, that the band extension is continuous in an appropriate sense.
Author: Wojciech Chachólski
Publisher: American Mathematical Soc.
ISBN: 0821827596
Category : Mathematics
Languages : en
Pages : 106
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Book Description
In this paper the authors develop homotopy theoretical methods for studying diagrams. In particular they explain how to construct homotopy colimits and limits in an arbitrary model category. The key concept introduced is that of a model approximation. A model approximation of a category $\mathcal{C}$ with a given class of weak equivalences is a model category $\mathcal{M}$ together with a pair of adjoint functors $\mathcal{M} \rightleftarrows \mathcal{C}$ which satisfy certain properties. The key result says that if $\mathcal{C}$ admits a model approximation then so does the functor category $Fun(I, \mathcal{C})$.
Author: Martina Brück
Publisher: American Mathematical Soc.
ISBN: 0821827537
Category : Mathematics
Languages : en
Pages : 111
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Book Description
This work is intended for graduate students and research mathematicians interested in differential geometry and partial differential equations.
