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

T. Hausel, M. Thaddeus, Journal of the American Mathematical Society 16 (2003) 303–329.


Journal Article | Published
Author
;
Abstract
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 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.
Publishing Year
Date Published
2003-04-01
Journal Title
Journal of the American Mathematical Society
Acknowledgement
The first author was supported by NSF grant DMS-97-29992. The second author was supported by NSF grant DMS-98-08529.
Volume
16
Issue
2
Page
303 - 329
IST-REx-ID

Cite this

Hausel T, Thaddeus M. Relations in the cohomology ring of the moduli space of rank 2 Higgs bundles. Journal of the American Mathematical Society. 2003;16(2):303-329. doi:10.1090/S0894-0347-02-00417-4
Hausel, T., & Thaddeus, M. (2003). Relations in the cohomology ring of the moduli space of rank 2 Higgs bundles. Journal of the American Mathematical Society, 16(2), 303–329. https://doi.org/10.1090/S0894-0347-02-00417-4
Hausel, Tamas, and Michael Thaddeus. “Relations in the Cohomology Ring of the Moduli Space of Rank 2 Higgs Bundles.” Journal of the American Mathematical Society 16, no. 2 (2003): 303–29. https://doi.org/10.1090/S0894-0347-02-00417-4.
T. Hausel and M. Thaddeus, “Relations in the cohomology ring of the moduli space of rank 2 Higgs bundles,” Journal of the American Mathematical Society, vol. 16, no. 2, pp. 303–329, 2003.
Hausel T, Thaddeus M. 2003. Relations in the cohomology ring of the moduli space of rank 2 Higgs bundles. Journal of the American Mathematical Society. 16(2), 303–329.
Hausel, Tamas, and Michael Thaddeus. “Relations in the Cohomology Ring of the Moduli Space of Rank 2 Higgs Bundles.” Journal of the American Mathematical Society, vol. 16, no. 2, American Mathematical Society, 2003, pp. 303–29, doi:10.1090/S0894-0347-02-00417-4.

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