##### Sesión Geometría y Topología

Diciembre 15, 15:30 ~ 15:50

## Stabilization of the Homotopy Groups of\\ the Moduli Spaces of $k$-Higgs Bundles

### Zúñiga-Rojas, Ronald Alberto

The work of Hausel proves that the Bia\l{}ynicki-Birula stratification of the moduli space of rank two Higgs bundles coincides with its Shatz stratification. He uses that to estimate some homotopy groups of the moduli spaces of $k$-Higgs bundles of rank two. Unfortunately, those two stratifications do not coincide in general. Here, the objective is to present a different proof of the stabilization of the homotopy groups of $\sM^k(2,d)$, and generalize it to $\sM^k(3,d)$, the moduli spaces of $k$-Higgs bundles of degree~$d$, and ranks two and three respectively, over a compact Riemann surface $X$, using the results from the works of Hausel and Thaddeus, among other tools.

Autores: Zúñiga-Rojas, Ronald Alberto.