Moving homology classes to infinity
-
Michael Farber
and
Dirk Schütz
Abstract
Let 
be a regular covering over a finite polyhedron with free abelian group of covering translations. Each nonzero cohomology class ξ ∈ H1(X;R) with q*ξ = 0 determines a notion of “infinity” of the noncompact space 
. In this paper we characterize homology classes z in which can be realized in arbitrary small neighborhoods of infinity in . This problem was motivated by applications in the theory of critical points of closed 1-forms initiated in [Farber M.: Zeros of closed 1-forms, homoclinic orbits and Lusternik-Schnirelman theory. Topol. Methods Nonlinear Anal. 19 (2002), 123–152], [Farber M.: Lusternik-Schnirelman theory and dynamics. Lusternik-Schnirelmann Category and Related Topics. Contemporary Mathematics 316 (2002), 95–111].
© Walter de Gruyter
Articles in the same Issue
- P-adic logarithmic forms and group varieties III
- Moving homology classes to infinity
- On a class of locally finite T-groups
- On Ext-universal modules in Gödel's universe
- Paraproducts in one and several parameters
- Labeled configuration spaces and group completions
- Universal localizations embedded in power-series rings
Articles in the same Issue
- P-adic logarithmic forms and group varieties III
- Moving homology classes to infinity
- On a class of locally finite T-groups
- On Ext-universal modules in Gödel's universe
- Paraproducts in one and several parameters
- Labeled configuration spaces and group completions
- Universal localizations embedded in power-series rings
