Mod p homology of unordered configuration spaces of  points in parallelizable surfac

Matthew Chen; Adela Yiyu Zhang

doi:10.1090/proc/16683

Mod p homology of unordered configuration spaces of points in parallelizable surfac

Matthew Chen, Adela Yiyu Zhang

Department of Mathematical Sciences

Research output: Contribution to journal › Journal article › Research › peer-review

1 Citation (Scopus)

7 Downloads (Pure)

Abstract

We provide a short proof that the dimensions of the mod p homology groups of the unordered configuration space B_k(T) of k points in a closed torus are the same as its Betti numbers for p > 2 and k ≤ p. Hence the integral homology has no p-power torsion in this range. The same argument works for the once-punctured genus g surface with g ≥ 0, thereby recovering a result of Brantner-Hahn-Knudsen via Lubin-Tate theory.

Original language	English
Journal	Proceedings of the American Mathematical Society
Volume	152
Issue number	5
Pages (from-to)	2239-2248
Number of pages	10
ISSN	0002-9939
DOIs	https://doi.org/10.1090/proc/16683
Publication status	Published - 2024

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© 2024 American Mathematical Society. All rights reserved.

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Cite this

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AB - We provide a short proof that the dimensions of the mod p homology groups of the unordered configuration space Bk(T) of k points in a closed torus are the same as its Betti numbers for p > 2 and k ≤ p. Hence the integral homology has no p-power torsion in this range. The same argument works for the once-punctured genus g surface with g ≥ 0, thereby recovering a result of Brantner-Hahn-Knudsen via Lubin-Tate theory.

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