Realisation of cycles by aspherical manifolds
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arXiv
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| Format: | Preprint |
| Publié: |
2008
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| _version_ | 1866913580344934400 |
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| author | Gaifullin, Alexander A. |
| author_facet | Gaifullin, Alexander A. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_0806_3580 |
| institution | arXiv |
| publishDate | 2008 |
| record_format | arxiv |
| spellingShingle | Realisation of cycles by aspherical manifolds Gaifullin, Alexander A. Algebraic Topology Geometric Topology 55N10, 57R95, 52B70 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. |
| title | Realisation of cycles by aspherical manifolds |
| topic | Algebraic Topology Geometric Topology 55N10, 57R95, 52B70 |
| url | https://arxiv.org/abs/0806.3580 |