scholarly journals Steenrod’s operations in simplicial Bredon-Illman cohomology with local coefficients

2011 ◽  
Vol 13 (1) ◽  
pp. 273-296 ◽  
Author(s):  
Goutam Mukherjee ◽  
Debasis Sen
Keyword(s):  
Local Coefficients ◽  
Cohomology With Local Coefficients

Whitney-sums (fibre-joins) in over space theory and obstruction theory for cohomology with local coefficients

1990 ◽  
Vol 115 (3-4) ◽  
pp. 359-365 ◽  
Author(s):  
John W. Rutter
Keyword(s):  
Obstruction Theory ◽  
Space Theory ◽  
Connected Space ◽  
Local Coefficient ◽  
General Properties ◽  
Local Coefficients ◽  
Simply Connected ◽  
Cohomology With Local Coefficients ◽  
Cohomology Sequence

SynopsisThe generalised Whitney sum (fibre-join) and the h-fibre-join can be defined in topM, the category of spaces over M. We note here some general properties of these constructions, and, as a specific example, we consider the relation between them and the extensions to the topM category of the top h-fibre-sequences F∗ΩB→E ∪ CF→B determined by top fibrations F→E→B. As an application we obtain the truncated local coefficient cohomology sequence for a top fibration which is topM principal fibration: this situation applies, for example, to the various stages of the Postnikov decomposition of a non-simply connected space X, and in this case we have M = K1(π1(X)).

scholarly journals Cohomology with local coefficients and knotted manifolds

2021 ◽  
Vol 107 ◽  
pp. 299-321
Author(s):  
Graham Ellis ◽  
Kelvin Killeen
Keyword(s):  
Local Coefficients ◽  
Cohomology With Local Coefficients

BREDON-ILLMAN COHOMOLOGY WITH LOCAL COEFFICIENTS

1996 ◽  
Vol 47 (2) ◽  
pp. 199-219 ◽  
Author(s):  
AMIYA MUKHERJEE ◽  
GOUTAM MUKHERJEE
Keyword(s):  
Local Coefficients ◽  
Cohomology With Local Coefficients

scholarly journals Segal's Spectral Sequence in Twisted Equivariant K-theory for Proper and Discrete Actions

2018 ◽  
Vol 61 (1) ◽  
pp. 121-150 ◽  
Author(s):  
Noé Bárcenas ◽  
Jesús Espinoza ◽  
Bernardo Uribe ◽  
Mario Velásquez
Keyword(s):  
Spectral Sequence ◽  
Finite Order ◽  
The Third ◽  
Bredon Cohomology ◽  
Discrete Torsion ◽  
Local Coefficients ◽  
K Theory ◽  
Cohomology With Local Coefficients

AbstractWe use a spectral sequence developed by Graeme Segal in order to understand the twisted G-equivariant K-theory for proper and discrete actions. We show that the second page of this spectral sequence is isomorphic to a version of Bredon cohomology with local coefficients in twisted representations. We furthermore explain some phenomena concerning the third differential of the spectral sequence, and recover known results when the twisting comes from finite order elements in discrete torsion.

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