Realisation of cycles by aspherical manifolds

Details Realisation of cycles by aspherical manifolds Realisation of cycles by aspherical manifolds

2008-06-22

arxiv.org/abs/0806.3580v1

Mathematics

Algebraic Topology

2 pages

Scientific paper

We develop a new purely combinatorial approach to N. Steenrod's problem on realisation of cycles. We prove that every n-dimensional homology class of every topological space can be realised with some multiplicity by an image of a finite-fold covering over the manifold M^n, where M^n is the isospectral manifold of real symmetric tridiagonal (n=1)x(n+1) matrices. In particular, every homology class of every arcwise connected topological space can be realised by a continuous image of an aspherical manifold.

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