Modular Representations of GL(n,FP) and Homotopy Theory

1985 ◽  
pp. 188-203 ◽  
Author(s):  
R. M. W. Wood
Keyword(s):  
Homotopy Theory ◽  
Modular Representations

HOMOLOGY DECOMPOSITIONS FOR CLASSIFYING SPACES OF FINITE GROUPS ASSOCIATED TO MODULAR REPRESENTATIONS

2001 ◽  
Vol 64 (2) ◽  
pp. 472-488 ◽  
Author(s):  
D. NOTBOHM
Keyword(s):  
Finite Group ◽  
Finite Groups ◽  
Homotopy Theory ◽  
Modular Representation ◽  
Modular Representations ◽  
Classifying Spaces ◽  
Modular Representation Theory ◽  
Classifying Space ◽  
Homotopy Colimit ◽  
A Finite Group

For a prime p, a homology decomposition of the classifying space BG of a finite group G consist of a functor F : D → spaces from a small category into the category of spaces and a map hocolim F → BG from the homotopy colimit to BG that induces an isomorphism in mod-p homology. Associated to a modular representation G → Gl(n; [ ]p), a family of subgroups is constructed that is closed under conjugation, which gives rise to three different homology decompositions, the so-called subgroup, centralizer and normalizer decompositions. For an action of G on an [ ]p-vector space V, this collection consists of all subgroups of G with nontrivial p-Sylow subgroup which fix nontrivial (proper) subspaces of V pointwise. These decomposition formulas connect the modular representation theory of G with the homotopy theory of BG.

Categorical Homotopy Theory

2009 ◽  
Author(s):  
Emily Riehl
Keyword(s):  
Homotopy Theory

On the Homotopy Theory of Arrangements

2018 ◽  
Author(s):  
Michael Falk ◽  
Richard Randell
Keyword(s):  
Homotopy Theory

On the homotopy theory of arrangements, II

2018 ◽  
Author(s):  
Michael Falk ◽  
Richard Randell
Keyword(s):  
Homotopy Theory

On equivariant disconnected rational homotopy theory

2010 ◽  
Vol 17 (2) ◽  
pp. 229-240
Author(s):  
Marek Golasiński
Keyword(s):  
Homotopy Theory ◽  
Weak Equivalence ◽  
Rational Homotopy Theory ◽  
Rational Homotopy ◽  
Hamiltonian Group ◽  
Simplicial Set ◽  
De Rham

Abstract An equivariant disconnected Sullivan–de Rham equivalence is developed using Kan's result on diagram categories. Given a finite Hamiltonian group G, let X be a G-simplicial set. It is shown that the associated system of algebras indexed by the category 𝒪(G) of a canonical orbit can be “approximated” (up to a weak equivalence) by such a system ℳ X with the properties required by nonequivariant minimal algebras.

scholarly journals A First Approximation to Homotopy Theory

1953 ◽  
Vol 39 (7) ◽  
pp. 655-660 ◽  
Author(s):  
E. H. Spanier ◽  
J. H. C. Whitehead
Keyword(s):  
Homotopy Theory ◽  
First Approximation

scholarly journals Modular representations of the ortho-symplectic supergroups

2007 ◽  
Vol 96 (1) ◽  
pp. 251-271 ◽  
Author(s):  
Bin Shu ◽  
Weiqiang Wang
Keyword(s):  
Modular Representations

scholarly journals The Picard Group of Equivariant Stable Homotopy Theory

2001 ◽  
Vol 163 (1) ◽  
pp. 17-33 ◽  
Author(s):  
H. Fausk ◽  
L.G. Lewis ◽  
J.P. May
Keyword(s):  
Homotopy Theory ◽  
Picard Group ◽  
Stable Homotopy ◽  
Stable Homotopy Theory ◽  
Equivariant Stable Homotopy
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