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arXiv · 0911.2749

The $S^1$-Equivariant Cohomology of Spaces of Long Exact Sequences

T. B. Williams
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Abstract

Let $S$ denote the graded polynomial ring $\C[x_1,...,x_m]$. We interpret a chain complex of free $S$-modules having finite length homology modules as an $S^1$-equivariant map $\C^m\sm\{0\} \to X$, where $X$ is a moduli space of exact sequences. By computing the cohomology of such spaces $X$ we obtain obstructions to such maps, including a slight generalization of the Herzog-Kühl equations.

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T. B. Williams. 2009-11-14. The $S^1$-Equivariant Cohomology of Spaces of Long Exact Sequences. https://arxiv.org/abs/0911.2749

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