Configuration Spaces Geometry, Combinatorics and Topology
These proceedings contain the contributions of some of the participants in the "intensive research period" held at the De Giorgi Research Center in Pisa, during the period May–June 2010. The central theme of this research period was the study of configura
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Configuration Spaces
7
Geometry, Combinatorics and Topology
edited by
9
A. Bjorner, F. Cohen, C. De Concini, C. Procesi and M. Salvetti
EDIZIONI DELLA NORMALE
14
CRM SERIES
Centro di Ricerca Matematica. . Ermio De GlOT91
Configuration Spaces Geometry, Combinatorics and Topology
edited by A. Bjorner, F. Cohen, C. De Concini, C. Procesi and M. Salvetti
EDIZIONI DELLA NORMALE
c 2012 Scuola Normale Superiore Pisa ISBN 978-88-7642-430-4 ISBN 978-88-7642-431-1 (eBook)
Contents
Authors’ affiliations
xv
Introduction
xix
Alejandro Adem and José Manuel Gómez On the structure of spaces of commuting elements in compact Lie groups
1 2 3 4 5 6
Introduction . . . . . . . . . . . . . . . . . . . . . . . Preliminaries on spaces of commuting elements . . . . Rational cohomology and path–connected components Stable splittings . . . . . . . . . . . . . . . . . . . . . Fundamental group . . . . . . . . . . . . . . . . . . . Equivariant K -theory . . . . . . . . . . . . . . . . . . 6.1 Finite abelian groups . . . . . . . . . . . . . . 6.2 Abelian groups of rank one . . . . . . . . . . . 6.3 Finitely generated abelian groups . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . .
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1 4 6 8 16 22 22 23 25 26
Meirav Amram, David Garber and Mina Teicher On the fundamental group of the complement of two real tangent conics and an arbitrary number of real tangent lines
1 Introduction . . . . . . . . . . . . . . . . . 2 Braid monodromy factorizations . . . . . . 3 The computation of the fundamental groups References . . . . . . . . . . . . . . . . . . . . .
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Dimitry Arinkin and Alexander Varchenko Intersection cohomology of a rank one local system on the complement of a hyperplane-like divisor
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27 30 34 46
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Anthony P. Bahri, Martin Bendersky, Frederick R. Cohen and Samuel Gitler A survey of some recent results concerning polyhedral products
1 Introduction . . . . . . . . . . . . 2 Definitions . . . . . . . . . . . . 3 Four examples . . . . . . . . . . . 4 Decompositions of suspensions . . 5 Applications to cohomology rings 6 Proof of a classical decomposition 7 Problems . . . . . . . . . . . . . References . . . . . . . . . . . . . . . .
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55 57 62 64 68 72 75 76
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81 84 84 87 87 90 91 92 93 94 94 96 99 101 102 102 105 106 107
Enrique Artal Bartolo, Jose Ignacio Cogolludo-Agustín and Anatoly Libgober Characters of fundamental groups of curve complements and orbifold pencils
1 2
Introduction . . . . . . . . . . . . . . . . . . . . . . . Preliminaries . . . . . . . . . . . . . . . . . . . . . . 2.1 Characteristic varieties . . . . . . . . . . . . . 2.2 Essential coordinate components . . . . . . .
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