The y-genus of the moduli space of PGL_n-Higgs bundles on a curve (for degree coprime to n)
Oscar Garc\'ia-Prada, Jochen Heinloth

TL;DR
This paper presents a recursive algorithm to compute the cohomology of moduli spaces of Higgs bundles on curves and applies it to determine the y-genus of PGL_n-Higgs bundles, confirming a conjecture.
Contribution
It introduces a new recursive method for cohomology computation and calculates the y-genus for PGL_n-Higgs bundles, validating a prior conjecture.
Findings
Recursive algorithm for cohomology of Higgs moduli spaces
Explicit computation of y-genus for PGL_n-Higgs bundles
Confirmation of Hausel's conjecture on y-genus
Abstract
Building on our previous joint work with A. Schmitt [7] we explain a recursive algorithm to determine the cohomology of moduli spaces of Higgs bundles on any given curve (in the coprime situation). As an application of the method we compute the y-genus of the space of PGL_n-Higgs bundles for any rank n, confirming a conjecture of T. Hausel.
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