{"doi":"10.4310/ATMP.1998.v2.n5.a3","status":"public","intvolume":" 2","publication_status":"published","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","day":"01","month":"09","date_published":"1998-09-01T00:00:00Z","date_updated":"2022-09-01T14:09:49Z","publication":"Advances in Theoretical and Mathematical Physics","author":[{"first_name":"Tamas","last_name":"Hausel","id":"4A0666D8-F248-11E8-B48F-1D18A9856A87","full_name":"Hausel, Tamas"}],"page":"1011 - 1040","type":"journal_article","quality_controlled":"1","issue":"5","article_type":"original","_id":"1450","external_id":{"arxiv":["math/9805071"]},"article_processing_charge":"No","publication_identifier":{"issn":["1095-0761"]},"publisher":"International Press","citation":{"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.","chicago":"Hausel, Tamás. “Vanishing of Intersection Numbers on the Moduli Space of Higgs Bundles.” *Advances in Theoretical and Mathematical Physics*. International Press, 1998. https://doi.org/10.4310/ATMP.1998.v2.n5.a3.","short":"T. Hausel, Advances in Theoretical and Mathematical Physics 2 (1998) 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. International Press, pp. 1011–1040, 1998.","apa":"Hausel, T. (1998). Vanishing of intersection numbers on the moduli space of Higgs bundles. *Advances in Theoretical and Mathematical Physics*. International Press. https://doi.org/10.4310/ATMP.1998.v2.n5.a3","mla":"Hausel, Tamás. “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.","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"},"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"}],"scopus_import":"1","publist_id":"5747","oa":1,"oa_version":"Preprint","acknowledgement":"First of all I would like to thank my supervisor Nigel Hitchin for suggesting Problem 1, and for his help and \r\n encouragement. I am grateful to Michael Thaddeus for his inspiring paper [Thai], enlightening communications and his constant interest in my work. I am also indebted to Manfred Lehn for the idea of the proof of Theorem 6.2. I have found\r\nconversations with Michael Atiyah, Frances Kirwan and Graeme Segal very stimulating. I thank the Mathematical Institute and St. Catherine's College, Oxford for their hospitality during the preparation of this work. Finally I thank Trinity College, Cambridge for financial support.","date_created":"2018-12-11T11:52:06Z","volume":2,"extern":"1","language":[{"iso":"eng"}],"main_file_link":[{"url":"http://arxiv.org/abs/math/9805071","open_access":"1"}],"year":"1998"}