Algebraic structures on cohomology of configuration spaces of manifolds with flows

Jordan S. Ellenberg; John D. Wiltshire-Gordon

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arXiv · 1508.02430

Algebraic structures on cohomology of configuration spaces of manifolds with flows

Jordan S. Ellenberg·John D. Wiltshire-Gordon

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Abstract

Let PConf^n M be the configuration space of ordered n-tuples of distinct points on a smooth manifold M admitting a nowhere-vanishing vector field. We show that the ith cohomology group with coefficients in a field H^i(PConf^n M, k) is an N-module, where N is the category of noncommutative finite sets introduced by Pirashvili and Richter. Studying the representation theory of N, we obtain new polynomiality results for the cohomology groups H^i(PConf^n M, k). In the case of unordered configuration space Conf^n M = (PConf^n M)/S_n and rational coefficients, we show that cohomology dimension in fixed degree is nondecreasing.

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BibTeX RIS

Jordan S. Ellenberg, John D. Wiltshire-Gordon. 2015-08-10. Algebraic structures on cohomology of configuration spaces of manifolds with flows. https://arxiv.org/abs/1508.02430

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