Getzler-Kapranov graph complex cohomology computations in weight 13
Marco Belli
TL;DR
This paper computes the weight-13 cohomology of moduli spaces of curves using the Getzler-Kapranov graph complex, focusing on specific genus and marked point pairs, advancing understanding of their algebraic structure.
Contribution
It provides explicit cohomology computations in weight 13 for moduli spaces of curves, extending previous theoretical results with concrete calculations.
Findings
Computed cohomology in weight 13 for specific (g, n) pairs
Extended the understanding of moduli space cohomology
Utilized Getzler-Kapranov graph complex for calculations
Abstract
We study the weight-graded compactly supported cohomology of the moduli spaces of curves using the Getzler-Kapranov graph complex. After recollecting the theory and some previous results, we compute the cohomology in weight 13 for the (g, n) pairs with 3g + 2n = 28.
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Taxonomy
TopicsAdvanced Combinatorial Mathematics · Commutative Algebra and Its Applications · Homotopy and Cohomology in Algebraic Topology