Wednesday, April 25, 2018
04/25/2018 - 4:15pm to 5:15pm
I will discuss the topology of a space of stable tropical curves of genus g with volume 1. The reduced rational homology of this space is canonically identified with the top weight cohomology of Mg and also with the homology of Kontsevich's graph complex. As one application, we show that H4g-6(Mg) isnonzero for infinitely many g. 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 a recent theorem of Willwacher, that homology of the graph complex vanishes in negative degrees, using the identifications above and known vanishing results for Mg. Joint work with M. Chan and S. Galatius.