LOCAL HOMOLOGY AND COHOMOLOGY, HOMOLOGY DIMENSION AND GENERALIZED MANIFOLDS

1975 ◽  
Vol 25 (3) ◽  
pp. 323-349 ◽  
Author(s):  
A È Harlap
Keyword(s):  
Local Homology ◽  
Generalized Manifolds

General position properties of ANR's

1982 ◽  
Vol 92 (3) ◽  
pp. 451-466 ◽  
Author(s):  
W. J. R. Mitchell
Keyword(s):  
Real Line ◽  
General Position ◽  
Cartesian Product ◽  
Vital Role ◽  
The Real ◽  
Homology Groups ◽  
Local Homology

This paper investigates the ‘general position’ properties which ANR's may possess. The most important of these is the disjoint discs property of Cannon (5), which plays a vital role in recent striking characterizations of manifolds (5, 9, 12, 18, 19, 22). Also considered are the property Δ of Borsuk(2) (which ensures an abundance of dimension-preserving maps), and the vanishing of local homology groups up to a given dimension (cf. (9)). Our main results give relations between these properties, and clarify their behaviour under the stabilization operation of taking cartesian product with the real line. In the last section these results are applied to give partial solutions to questions about homogeneous ANR's.

Generalized Co-Cohen–Macaulay and Co-Buchsbaum Modules

2007 ◽  
Vol 14 (02) ◽  
pp. 265-278
Author(s):  
Nguyen Tu Cuong ◽  
Nguyen Thi Dung ◽  
Le Thanh Nhan
Keyword(s):  
Artinian Modules ◽  
Basic Properties ◽  
Local Homology

We study two classes of Artinian modules called co-Buchsbaum modules and generalized co-Cohen–Macaulay modules. Some basic properties and characterizations of these modules in terms of 𝔮-weak co-sequences, co-standard sequences, multiplicity, local homology modules are presented.

Some properties of local homology and local cohomology modules

2013 ◽  
Vol 50 (1) ◽  
pp. 129-141
Author(s):  
Tran Nam
Keyword(s):  
Local Cohomology ◽  
Local Homology ◽  
Local Cohomology Modules ◽  
Cohomology Modules ◽  
Compact Module

We study some properties of representable or I-stable local homology modules HiI (M) where M is a linearly compact module. By duality, we get some properties of good or at local cohomology modules HIi (M) of A. Grothendieck.

Formal local homology

2021 ◽  
Vol 163 (2) ◽  
pp. 267-284
Author(s):  
Tran Tuan Nam ◽  
Do Ngoc Yen ◽  
Nguyen Minh Tri
Keyword(s):  
Local Homology

Some Characterizations of Generalized Manifolds With Boundaries

1952 ◽  
Vol 4 ◽  
pp. 329-342 ◽  
Author(s):  
Paul A. White
Keyword(s):  
Manifolds With Boundary ◽  
Manifold With Boundary ◽  
Generalized Manifolds ◽  
Definition Of

In R. L. Wilder's book [2] the open and closed generalized manifolds are extensively studied. However, no study is made of the generalized manifold with boundary nor is a definition of such a space given except in the case of the generalized closed n-cell. A definition of a generalized manifold with boundary was given by the author in his paper [1]. Before undertaking the study of further properties of these manifolds it seems appropriate to characterize the manifolds with boundary in terms of the open and closed manifolds of Wilder. It is to that purpose that this paper is directed and in particular the generalized closed n-cell of Wilder is characterized as a special manifold with boundary.

scholarly journals On the iterated Hamiltonian Floer homology

2020 ◽  
pp. 2050026
Author(s):  
Erman Çı̇nelı̇ ◽  
Viktor L. Ginzburg
Keyword(s):  
Fixed Point ◽  
Euler Characteristic ◽  
Group Action ◽  
Floer Homology ◽  
Local Homology ◽  
Lefschetz Index ◽  
Cyclic Group Action ◽  
Symplectically Aspherical Manifold ◽  
Aspherical Manifold ◽  
Symplectically Aspherical

The focus of the paper is the behavior under iterations of the filtered and local Floer homology of a Hamiltonian on a symplectically aspherical manifold. The Floer homology of an iterated Hamiltonian comes with a natural cyclic group action. In the filtered case, we show that the supertrace of a generator of this action is equal to the Euler characteristic of the homology of the un-iterated Hamiltonian. For the local homology the supertrace is the Lefschetz index of the fixed point. We also prove an analog of the classical Smith inequality for the iterated local homology and the equivariant versions of these results.

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