Mod p homology of unordered configuration spaces of surfaces

2022/08/22 by Chen, Matthew, Zhang, Adela YiYu
#Algebraic Topology (math.AT) #FOS: Mathematics

paper · doi:10.48550/arxiv.2208.10293

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 torus are the same as its Betti numbers for p>2 and k≤ p. Hence the integral homology has no p-power torsion. The same argument works for the punctured genus g surface with g>0, thereby recovering a result of Brantner-Hahn-Knudsen via Lubin-Tate theory.

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