Explicit construction of manifolds realizing the prescribed homology classes
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2007
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866916487131824128 |
|---|---|
| author | Gaifullin, A. A. |
| author_facet | Gaifullin, A. A. |
| contents | We consider a classical N. Steenrod's problem on realization of homology classes by images of the fundamental classes of manifolds. It is well-known that each integral homology class can be realized with some multiplicity as an image of the fundamental class of a manifold. Our main result is an explicit purely combinatorial construction that for a given integral cycle provides a combinatorial manifold realizing a multiple of the homology class of this cycle. The construction is based on a local procedure for resolving singularities of a pseudo-manifold. We give an application of our result to the problem of constructing a combinatorial manifold with the prescribed set of links of vertices. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_0712_1709 |
| institution | arXiv |
| publishDate | 2007 |
| record_format | arxiv |
| spellingShingle | Explicit construction of manifolds realizing the prescribed homology classes Gaifullin, A. A. Geometric Topology Combinatorics 57R95, 52B05 We consider a classical N. Steenrod's problem on realization of homology classes by images of the fundamental classes of manifolds. It is well-known that each integral homology class can be realized with some multiplicity as an image of the fundamental class of a manifold. Our main result is an explicit purely combinatorial construction that for a given integral cycle provides a combinatorial manifold realizing a multiple of the homology class of this cycle. The construction is based on a local procedure for resolving singularities of a pseudo-manifold. We give an application of our result to the problem of constructing a combinatorial manifold with the prescribed set of links of vertices. |
| title | Explicit construction of manifolds realizing the prescribed homology classes |
| topic | Geometric Topology Combinatorics 57R95, 52B05 |
| url | https://arxiv.org/abs/0712.1709 |