Tropical curves, graph complexes, and top weight cohomology of ℳ_{ℊ}
| Autor: | Sam Payne, Melody Chan, Søren Galatius |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
Applied Mathematics
General Mathematics 010102 general mathematics Geometric Topology (math.GT) Mathematics::Geometric Topology 01 natural sciences Graph Cohomology Combinatorics Mathematics - Algebraic Geometry Mathematics - Geometric Topology Mathematics::K-Theory and Homology 0103 physical sciences FOS: Mathematics Algebraic Topology (math.AT) Mathematics - Algebraic Topology 010307 mathematical physics 0101 mathematics Algebraic Geometry (math.AG) Mathematics |
| Zdroj: | Journal of the American Mathematical Society. 34:565-594 |
| ISSN: | 1088-6834 0894-0347 |
| DOI: | 10.1090/jams/965 |
| Popis: | We study the topology of a space parametrizing stable tropical curves of genus g with volume 1, showing that its reduced rational homology is canonically identified with both the top weight cohomology of M_g and also with the genus g part of the homology of Kontsevich's graph complex. Using a theorem of Willwacher relating this graph complex to the Grothendieck-Teichmueller Lie algebra, we deduce that H^{4g-6}(M_g;Q) is nonzero for g=3, g=5, and g at least 7. This disproves a recent conjecture of Church, Farb, and Putman as well as an older, more general conjecture of Kontsevich. We also give an independent proof of another theorem of Willwacher, that homology of the graph complex vanishes in negative degrees. 31 pages. v2: streamlined exposition. Final version, to appear in J. Amer. Math. Soc |
| Databáze: | OpenAIRE |
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