Properties of the basic cohomology of transversely Kähler foliations

1991 ◽  
Vol 40 (2) ◽  
pp. 177-188 ◽  
Author(s):  
Luis A. Cordero ◽  
Robert A. Wolak
Keyword(s):  
Basic Cohomology

scholarly journals Equivariant basic cohomology under deformations

2021 ◽  
Author(s):  
Francisco C. Caramello ◽  
Dirk Töben
Keyword(s):  
Basic Cohomology

scholarly journals Basic cohomology of associative algebras

1996 ◽  
Vol 114 (1) ◽  
pp. 39-50 ◽  
Author(s):  
Michel Dubois-Violette ◽  
Thierry Masson
Keyword(s):  
Associative Algebras ◽  
Basic Cohomology

scholarly journals The basic cohomology of the twisted N=16, D=2 super-Maxwell theory

2003 ◽  
Vol 575 (3-4) ◽  
pp. 349-357
Author(s):  
B. Geyer ◽  
D. Mülsch
Keyword(s):  
Maxwell Theory ◽  
Basic Cohomology

scholarly journals Equivariant basic cohomology of Riemannian foliations

2018 ◽  
Vol 2018 (745) ◽  
pp. 1-40 ◽  
Author(s):  
Oliver Goertsches ◽  
Dirk Töben
Keyword(s):  
Fixed Point ◽  
Lie Group ◽  
Betti Number ◽  
Group Actions ◽  
Fixed Point Set ◽  
Foliated Manifold ◽  
Riemannian Foliations ◽  
Basic Cohomology ◽  
Lie Group Actions ◽  
Point Set

Abstract The basic cohomology of a complete Riemannian foliation with all leaves closed is the cohomology of the leaf space. In this paper we introduce various methods to compute the basic cohomology in the presence of both closed and non-closed leaves in the simply-connected case (or more generally for Killing foliations): We show that the total basic Betti number of the union C of the closed leaves is smaller than or equal to the total basic Betti number of the foliated manifold, and we give sufficient conditions for equality. If there is a basic Morse–Bott function with critical set equal to C, we can compute the basic cohomology explicitly. Another case in which the basic cohomology can be determined is if the space of leaf closures is a simple, convex polytope. Our results are based on Molino’s observation that the existence of non-closed leaves yields a distinguished transverse action on the foliated manifold with fixed point set C. We introduce equivariant basic cohomology of transverse actions in analogy to equivariant cohomology of Lie group actions enabling us to transfer many results from the theory of Lie group actions to Riemannian foliations. The prominent role of the fixed point set in the theory of torus actions explains the relevance of the set C in the basic setting.

scholarly journals Basic Cohomology Group Decomposition of K-Contact 5-Manifolds

2016 ◽  
Vol 71 (3-4) ◽  
pp. 1023-1030
Author(s):  
Jiuru Zhou ◽  
Peng Zhu
Keyword(s):  
Cohomology Group ◽  
Basic Cohomology

scholarly journals Modified Differentials and Basic Cohomology for Riemannian Foliations

2011 ◽  
Vol 23 (3) ◽  
pp. 1314-1342 ◽  
Author(s):  
Georges Habib ◽  
Ken Richardson
Keyword(s):  
Riemannian Foliations ◽  
Basic Cohomology
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