Zk-stratifolds

Ángel, Andrés; Torres, Arley Fernando; Segovia, Carlos

doi:10.2140/agt.2024.24.1863

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Z_k-stratifolds

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Ángel, Andrés
Max Planck Institute for Mathematics, Max Planck Society;

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https://doi.org/10.48550/arXiv.1810.00531
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Angel-Segovia-Torres_Zk-stratifolds_2024.pdf
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Citation

Ángel, A., Torres, A. F., & Segovia, C. (2024). Z_k-stratifolds. Algebraic & Geometric Topology, 24(4), 1863-1901. doi:10.2140/agt.2024.24.1863.

Cite as: https://hdl.handle.net/21.11116/0000-000F-D677-A

Abstract

Generalizing the ideas of Zk–manifolds from Sullivan and stratifolds from Kreck, we define Zk–stratifolds. We show that the bordism theory of Zk–stratifolds is sufficient to represent all homology classes of a CW–complex with coefficients in Zk. We present a geometric interpretation of the Bockstein long exact sequences and the Atiyah–Hirzebruch spectral sequence for Zk–bordism for k an odd number. Finally, for p an odd prime, we give geometric representatives of all classes in H∗(BZp;Zp) using Zp–stratifolds.