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On p ‐Completed Classifying Spaces of Discrete Groups and Finite Complexes
Author(s) -
Levi Ran
Publication year - 1999
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/s0024610799007279
Subject(s) - cohomological dimension , dimension (graph theory) , retract , mathematics , space (punctuation) , loop (graph theory) , pure mathematics , group (periodic table) , classifying space , topology (electrical circuits) , algebra over a field , combinatorics , computer science , physics , cohomology , quantum mechanics , operating system , homotopy
It is shown that for certain discrete p ‐perfect groups G , in particular for all p ‐perfect finite groups and certain groups of finite virtual cohomological dimension, the loop space on the p ‐completed classifying space Ω B G p ^is a retract of the loop space on the p ‐completion of a certain finite complex. For those finite virtual cohomological dimension groups where the author's methods apply, a bound on the dimension of such a complex is provided.