Complex Vasquez invariant

2023/09/24 by Gąsior, Anna, Lutowski, Rafał
#20C10 #20H15 Secondary: 32Q55 #32G05 #Algebraic Topology (math.AT) #FOS: Mathematics #Primary: 32Q15

paper · doi:10.48550/arxiv.2309.13740

Abstract

In 1970 Vasquez proved that to every finite group G we can assign a natural number n(G) with the property that every flat manifold with holonomy G is a total space of a fiber bundle, with the fiber being a flat torus and the base space -- a flat manifold of dimension less than or equal to n(G). In particular, this means that the characteristic algebra of any flat manifold with holonomy G vanishes in dimension greater than n(G). We define a complex analog of Vasquez invariant, in which finite groups are considered as holonomy groups of compact flat Kähler manifolds.

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