Geodesic
Topology of Hitchin systems and Hodge theory of character varieties: the case $A_1$
Mark Andrea A. de Cataldo1 ; Tamás Hausel2 ; Luca Migliorini3
1 Department of Mathematics, Stony Brook University, Stony Brook, NY 11794-3651
2 Mathematical Institute, University of Oxford, 24-20 St. Giles', Oxford OX1 3LB, United Kingdom
3 Dipartimento de Matematica, Università di Bologna, Piazza di Porta S. Donato, 5, 40127 Bologna, Italy
Annals of mathematics, Tome 175 (2012) no. 3, pp. 1329-1407.

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For $\mathrm{G}=\mathrm{GL}_2,\mathrm{PGL}_2, \mathrm{SL}_2$ we prove that the perverse filtration associated with the Hitchin map on the rational cohomology of the moduli space of twisted $\mathrm{G}$-Higgs bundles on a compact Riemann surface $C$ agrees with the weight filtration on the rational cohomology of the twisted $\mathrm{G}$ character variety of $C$ when the cohomologies are identified via non-Abelian Hodge theory. The proof is accomplished by means of a study of the topology of the Hitchin map over the locus of integral spectral curves.
DOI : 10.4007/annals.2012.175.3.7

Mark Andrea A. de Cataldo 1 ; Tamás Hausel 2 ; Luca Migliorini 3

1 Department of Mathematics, Stony Brook University, Stony Brook, NY 11794-3651
2 Mathematical Institute, University of Oxford, 24-20 St. Giles', Oxford OX1 3LB, United Kingdom
3 Dipartimento de Matematica, Università di Bologna, Piazza di Porta S. Donato, 5, 40127 Bologna, Italy 
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     title = {Topology of {Hitchin} systems and  {Hodge} theory of character varieties: the case $A_1$},
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Mark Andrea A. de Cataldo; Tamás Hausel; Luca Migliorini. Topology of Hitchin systems and  Hodge theory of character varieties: the case $A_1$. Annals of mathematics, Tome 175 (2012) no. 3, pp. 1329-1407. doi : 10.4007/annals.2012.175.3.7. http://geodesic.mathdoc.fr/articles/10.4007/annals.2012.175.3.7/

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