Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8255673 | Journal of Geometry and Physics | 2018 | 15 Pages |
Abstract
Consider a Riemann surface X of genus gâ¥2 equipped with an antiholomorphic involution Ï. This induces a natural involution on the moduli space M(r,d) of semistable Higgs bundles of rank r and degree d. If D is a divisor such that Ï(D)=D, this restricts to an involution on the moduli space M(r,D) of those Higgs bundles with fixed determinant O(D) and trace-free Higgs field. The fixed point sets of these involutions M(r,d)Ï and M(r,D)Ï are (A,A,B)-branes introduced by Baraglia and Schaposnik (2016). In this paper, we derive formulas for the mod 2 Betti numbers of M(r,d)Ï and M(r,D)Ï when r=2 and d is odd. In the course of this calculation, we also compute the mod 2 cohomology ring of Symm(X)Ï, the fixed point set of the involution induced by Ï on symmetric products of the Riemann surface.
Keywords
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Physical Sciences and Engineering
Mathematics
Mathematical Physics
Authors
Thomas John Baird,