Lattice Spectral Sequences and Cohomology of Configuration Spaces

Philip Tosteson

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arXiv · 1612.06034

Lattice Spectral Sequences and Cohomology of Configuration Spaces

Philip Tosteson

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Abstract

For a topological space $X$, we introduce a criterion for the $\rm FI$ module $H^i({\rm Conf}_n(X))$ to be finitely generated and give several applications. For instance, if $C$ is a finite connected $CW$ complex, then $X = C \times \mathbb{R}^2$ satisfies the criterion. Our main tool is a spectral sequence that we derive from the homological algebra of the partition lattice.

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BibTeX RIS

Philip Tosteson. 2016-12-19. Lattice Spectral Sequences and Cohomology of Configuration Spaces. https://arxiv.org/abs/1612.06034

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