On discontinuities of cocycles in cohomology theories for topological groups

2011/12/07 by Tim Austin, Austin, Tim
Mathematics · #18G10 #20J06 #22D05 #FOS: Mathematics #General Topology (math.GN) #Group Theory (math.GR) #K-Theory and Homology (math.KT) #math.GN #math.GR #math.KT #msc:18G10 #msc:20J06 #msc:22D05

paper · pdf · doi:10.48550/arxiv.1112.1465

42 pages, 1 figure [TDA May 1, 2012] Replaced with a substantially new argument, which also fixes some howlers in the first version. [TDA June 13, 2012] Some minor corrections and editing

arxiv created 2012/06/13 · arxiv updated 2012/06/14

Abstract

This paper studies Moore's measurable cohomology theory for locally compact groups and Polish modules. An elementary dimension-shifting argument is used to show that all classes in that theory have representatives with considerable extra topological structure beyond measurability. Using this, for certain target modules one can also construct a direct comparison map with a different cohomology theory for topological groups defined by Segal, and show that this map is an isomorphism.

Related

• On Cohomology theory for topological groups
• On the vanishing of the measurable Schur cohomology groups of Weil groups
• An uncountable Moore-Schmidt theorem
• A Cocycle Model for Topological and Lie Group Cohomology
• Continuous cochains on Furstenberg boundaries and injectivity of the comparison map