scholarly journals Relative cohomology theory for profinite groups

2019 ◽  
Vol 223 (4) ◽  
pp. 1617-1688
Author(s):  
Gareth Wilkes
Keyword(s):  
Cohomology Theory ◽  
Profinite Groups ◽  
Relative Cohomology

scholarly journals On the Cohomology of Relative Babach Algebras

2019 ◽  
Vol 13 (10) ◽  
pp. 1
Author(s):  
Alaa Hassan Noreldeen Mohamed
Keyword(s):  
Banach Algebra ◽  
Cohomology Theory ◽  
Basic Theorem ◽  
Relative Cohomology

We study the relative cohomology theory of Banach algebra and give some important basic theorem of it. More, we give discuss about some of properties which we require it in our investigation. At long last, we ponder the dihedral cohomology aggregate as definitions and hypotheses and we characterize the Banach S-relative dihedral cohomology gathering and some theorems.

Relative Cohomology

1957 ◽  
Vol 9 ◽  
pp. 19-34 ◽  
Author(s):  
D. G. Higman
Keyword(s):  
Cohomology Theory ◽  
Cohomology Groups ◽  
Dual Pairs ◽  
Relative Cohomology

It is our purpose in this paper to present certain aspects of a cohomology theory of a ring R relative to a subring S, basing the theory on the notions of induced and produced pairs of our earlier paper (2), but making the paper self-contained except for references to a few specific results of (2). The cohomology groups introduced occur in dual pairs. Generic cocycles are defined, and the groups are related to the protractions and retractions of R-modules.

scholarly journals Coarse cohomology with twisted coefficients

2020 ◽  
Vol 70 (6) ◽  
pp. 1413-1444
Author(s):  
Elisa Hartmann
Keyword(s):  
Sheaf Cohomology ◽  
Grothendieck Topology ◽  
Coarse Structure ◽  
Relative Cohomology ◽  
Number Of Ends ◽  
Constant Coefficients ◽  
Coarse Space ◽  
Grothendieck Topologies

AbstractTo a coarse structure we associate a Grothendieck topology which is determined by coarse covers. A coarse map between coarse spaces gives rise to a morphism of Grothendieck topologies. This way we define sheaves and sheaf cohomology on coarse spaces. We obtain that sheaf cohomology is a functor on the coarse category: if two coarse maps are close they induce the same map in cohomology. There is a coarse version of a Mayer-Vietoris sequence and for every inclusion of coarse spaces there is a coarse version of relative cohomology. Cohomology with constant coefficients can be computed using the number of ends of a coarse space.

Stable decompositions of classifying spaces of finite abelianp-groups

1988 ◽  
Vol 103 (3) ◽  
pp. 427-449 ◽  
Author(s):  
John C. Harris ◽  
Nicholas J. Kuhn
Keyword(s):  
Finite Group ◽  
Cohomology Theory ◽  
Classifying Spaces ◽  
Classifying Space ◽  
Image Position ◽  
A Finite Group

LetBGbe the classifying space of a finite groupG. Consider the problem of finding astabledecompositionintoindecomposablewedge summands. Such a decomposition naturally splitsE*(BG), whereE* is any cohomology theory.

Burnside algebras of profinite groups

1994 ◽  
Vol 22 (5) ◽  
pp. 1551-1575 ◽  
Author(s):  
R.S. Pierce
Keyword(s):  
Profinite Groups

scholarly journals WITTEN DEFORMATION FOR NONCOMPACT MANIFOLDS WITH BOUNDED GEOMETRY

2021 ◽  
pp. 1-38
Author(s):  
Xianzhe Dai ◽  
Junrong Yan
Keyword(s):  
Essential Role ◽  
Morse Function ◽  
Noncompact Manifold ◽  
Morse Inequalities ◽  
Bounded Geometry ◽  
Noncompact Manifolds ◽  
Witten Laplacian ◽  
Relative Cohomology ◽  
Witten Deformation ◽  
Small Eigenvalues

Abstract Motivated by the Landau–Ginzburg model, we study the Witten deformation on a noncompact manifold with bounded geometry, together with some tameness condition on the growth of the Morse function f near infinity. We prove that the cohomology of the Witten deformation $d_{Tf}$ acting on the complex of smooth $L^2$ forms is isomorphic to the cohomology of the Thom–Smale complex of f as well as the relative cohomology of a certain pair $(M, U)$ for sufficiently large T. We establish an Agmon estimate for eigenforms of the Witten Laplacian which plays an essential role in identifying these cohomologies via Witten’s instanton complex, defined in terms of eigenspaces of the Witten Laplacian for small eigenvalues. As an application, we obtain the strong Morse inequalities in this setting.

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