(\mathbb{Z}_k\)-stratifolds
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}...
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| creator | Angel, Andrés Torres, Arley Fernando Segovia, Carlos |
| description | 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. |
| doi_str_mv | 10.48550/arxiv.1810.00531 |
| format | Article |
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| subjects | Homology |
| title | (\mathbb{Z}_k\)-stratifolds |
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