Relations in the cohomology ring of the moduli space of rank 2 Higgs bundles

Journal article

The moduli space of stable bundles of rank 2 and degree 1 on a Riemann surface has rational cohomology generated by the so-called universal classes. The work of Baranovsky, King-Newstead, Siebert-Tian 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 non-compact 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.

Authors: Hausel, T; Thaddeus, M

• Publication status: Published
• Journal: JOURNAL OF THE AMERICAN MATHEMATICAL SOCIETY
• Volume: 16
• Issue: 2
• Pages: 303-329
• Publication date: 2000-03-16
• DOI: 10.1090/S0894-0347-02-00417-4
• ISSN: 0894-0347
• Language: English
• Keywords: math-ph; 14H60 (Primary) 14D20, 14H81, 32Q55, 58D27 (Secondary); math.MP; math.AG; math.DG; math.SG