Year: 2024
Type: article
Abstract: We study the weight 2 graded piece of the compactly supported rational cohomology of the moduli spaces of curves Mg,n and show that this can be computed as the cohomology of a graph complex that is closely related to graph complexes arising in the study of embedding spaces. For n=0, we express this cohomology in terms of W0Hc∙(Mg′,n′) for g′≤g and n′≤2, and thereby produce several new infinite families of nonvanishing unstable cohomology groups on Mg, including the first such families in odd degrees. In particular, we show that dimH4g−k(Mg) grows at least exponentially with g for k∈{8,9,11,12,14,15,16,18,19}.
Source: Duke Mathematical Journal
Authors: Sam Payne, Thomas Willwacher
Institutions: The University of Texas at Austin, ETH Zurich
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4406038835