$\mathbb{Z}_k$-stratifolds
Fuente:
arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2018
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| _version_ | 1866916331961450496 |
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| author | Angel, Andrés Torres, Arley Fernando Segovia, Carlos |
| author_facet | Angel, Andrés Torres, Arley Fernando Segovia, Carlos |
| contents | Generalizing the ideas of $\mathbb{Z}_k$-manifolds from Sullivan and stratifolds from Kreck, we define $\mathbb{Z}_k$-stratifolds. We show that the bordism theory of $\mathbb{Z}_k$-stratifolds is sufficient to represent all homology classes of a $CW$-complex with coefficients in $\mathbb{Z}_k$. We present a geometric interpretation of the Bockstein long exact sequences and the Atiyah-Hirzebruch spectral sequence for $\mathbb{Z}_k$-bordism ($k$ an odd number). Finally, for $p$ an odd prime, we give geometric representatives of all classes in $H_*(B\mathbb{Z}_p;\mathbb{Z}_p)$ using $\mathbb{Z}_p$-stratifolds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1810_00531 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | $\mathbb{Z}_k$-stratifolds Angel, Andrés Torres, Arley Fernando Segovia, Carlos Algebraic Topology Generalizing the ideas of $\mathbb{Z}_k$-manifolds from Sullivan and stratifolds from Kreck, we define $\mathbb{Z}_k$-stratifolds. We show that the bordism theory of $\mathbb{Z}_k$-stratifolds is sufficient to represent all homology classes of a $CW$-complex with coefficients in $\mathbb{Z}_k$. We present a geometric interpretation of the Bockstein long exact sequences and the Atiyah-Hirzebruch spectral sequence for $\mathbb{Z}_k$-bordism ($k$ an odd number). Finally, for $p$ an odd prime, we give geometric representatives of all classes in $H_*(B\mathbb{Z}_p;\mathbb{Z}_p)$ using $\mathbb{Z}_p$-stratifolds. |
| title | $\mathbb{Z}_k$-stratifolds |
| topic | Algebraic Topology |
| url | https://arxiv.org/abs/1810.00531 |