Moving homology classes to infinity

Michael Farber*, Dirk Schütz

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


Let q : X̃ → X 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 X̃. In this paper we characterize homology classes z in X̃ which can be realized in arbitrary small neighborhoods of infinity in X̃. 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].

Original languageEnglish
Pages (from-to)281-296
Number of pages16
JournalForum Mathematicum
Issue number2
StatePublished - 20 Mar 2007
Externally publishedYes


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