Relations in the cohomology ring of the moduli space of rank 2 Higgs bundles
Abstract
The moduli space of stable bundles of rank 2 and degree 1 on a Riemann surface has rational cohomology generated by the socalled universal classes. The work of Baranovsky, KingNewstead, SiebertTian and Zagier provided a complete set of relations between these classes, expressed in terms of a recursion in the genus. This paper accomplishes the same thing for the noncompact moduli spaces of Higgs bundles, in the sense of Hitchin and Simpson. There are many more independent relations than for stable bundles, but in a sense the answer is simpler, since the formulas are completely explicit, not recursive. The results of Kirwan on equivariant cohomology for holomorphic circle actions are of key importance. Together, Parts I and II describe the cohomology rings of spaces of rank 2 Higgs bundles at essentially the same level of detail as is known for stable bundles.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 March 2000
 arXiv:
 arXiv:math/0003094
 Bibcode:
 2000math......3094H
 Keywords:

 Mathematics  Algebraic Geometry;
 Mathematical Physics;
 Mathematics  Differential Geometry;
 Mathematics  Mathematical Physics;
 Mathematics  Symplectic Geometry;
 14H60 (Primary) 14D20;
 14H81;
 32Q55;
 58D27 (Secondary)
 EPrint:
 31 pages, LaTeX. Changes in title and introduction only