{"date_updated":"2019-04-26T07:22:03Z","extern":1,"year":"1998","title":"Vanishing of intersection numbers on the moduli space of Higgs bundles","abstract":[{"text":"In this paper we consider the topological side of a problem which is the analogue of Sen's S-duality testing conjecture for Hitchin's moduli space M of rank 2 stable Higgs bundles of fixed determinant of odd degree over a Riemann surface ∑. We prove that all intersection numbers in the compactly supported cohomology of M vanish, i.e. "there are no topological L2 harmonic forms on M". This result generalizes the well known vanishing of the Euler characteristic of the moduli space of rank 2 stable bundles N of fixed determinant of odd degree over ∑. Our proof shows that the vanishing of all intersection numbers of H* cpt(M) is given by relations analogous to the Mumford relations in the cohomology ring of N.","lang":"eng"}],"volume":2,"intvolume":" 2","page":"1011 - 1040","issue":"5","doi":"10.4310/ATMP.1998.v2.n5.a3","main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/math/9805071"}],"publisher":"International Press","publist_id":"5747","status":"public","publication":"Advances in Theoretical and Mathematical Physics","oa":1,"type":"journal_article","month":"09","_id":"1450","day":"01","date_published":"1998-09-01T00:00:00Z","citation":{"chicago":"Hausel, Tamas. “Vanishing of Intersection Numbers on the Moduli Space of Higgs Bundles.” *Advances in Theoretical and Mathematical Physics* 2, no. 5 (1998): 1011–40. https://doi.org/10.4310/ATMP.1998.v2.n5.a3.","apa":"Hausel, T. (1998). Vanishing of intersection numbers on the moduli space of Higgs bundles. *Advances in Theoretical and Mathematical Physics*, *2*(5), 1011–1040. https://doi.org/10.4310/ATMP.1998.v2.n5.a3","ista":"Hausel T. 1998. Vanishing of intersection numbers on the moduli space of Higgs bundles. Advances in Theoretical and Mathematical Physics. 2(5), 1011–1040.","ieee":"T. Hausel, “Vanishing of intersection numbers on the moduli space of Higgs bundles,” *Advances in Theoretical and Mathematical Physics*, vol. 2, no. 5, pp. 1011–1040, 1998.","ama":"Hausel T. Vanishing of intersection numbers on the moduli space of Higgs bundles. *Advances in Theoretical and Mathematical Physics*. 1998;2(5):1011-1040. doi:10.4310/ATMP.1998.v2.n5.a3","short":"T. Hausel, Advances in Theoretical and Mathematical Physics 2 (1998) 1011–1040.","mla":"Hausel, Tamas. “Vanishing of Intersection Numbers on the Moduli Space of Higgs Bundles.” *Advances in Theoretical and Mathematical Physics*, vol. 2, no. 5, International Press, 1998, pp. 1011–40, doi:10.4310/ATMP.1998.v2.n5.a3."},"quality_controlled":0,"author":[{"last_name":"Hausel","id":"4A0666D8-F248-11E8-B48F-1D18A9856A87","full_name":"Tamas Hausel","first_name":"Tamas"}],"publication_status":"published","date_created":"2018-12-11T11:52:06Z"}