Abstract
Let q : X → X be a regular covering over a finite polyhedron with free abelian group of covering translations. Each nonzero cohomology class ξ ∈ H(X;R) with q∗ξ = 0 determines a notion of “infinity” of the noncompact space X. In this paper we characterize homology classes z in X which can be realized in arbitrary small neighborhoods of infinity in X. This problem was motivated by applications in the theory of critical points of closed 1-forms initiated in [2], [3].
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