{"issue":"5","type":"journal_article","publisher":"International Press","external_id":{"arxiv":["math/9805071"]},"language":[{"iso":"eng"}],"citation":{"apa":"Hausel, T. (1998). Vanishing of intersection numbers on the moduli space of Higgs bundles. <i>Advances in Theoretical and Mathematical Physics</i>. International Press. <a href=\"https://doi.org/10.4310/ATMP.1998.v2.n5.a3\">https://doi.org/10.4310/ATMP.1998.v2.n5.a3</a>","mla":"Hausel, Tamás. “Vanishing of Intersection Numbers on the Moduli Space of Higgs Bundles.” <i>Advances in Theoretical and Mathematical Physics</i>, vol. 2, no. 5, International Press, 1998, pp. 1011–40, doi:<a href=\"https://doi.org/10.4310/ATMP.1998.v2.n5.a3\">10.4310/ATMP.1998.v2.n5.a3</a>.","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,” <i>Advances in Theoretical and Mathematical Physics</i>, vol. 2, no. 5. International Press, pp. 1011–1040, 1998.","chicago":"Hausel, Tamás. “Vanishing of Intersection Numbers on the Moduli Space of Higgs Bundles.” <i>Advances in Theoretical and Mathematical Physics</i>. International Press, 1998. <a href=\"https://doi.org/10.4310/ATMP.1998.v2.n5.a3\">https://doi.org/10.4310/ATMP.1998.v2.n5.a3</a>.","short":"T. Hausel, Advances in Theoretical and Mathematical Physics 2 (1998) 1011–1040.","ama":"Hausel T. Vanishing of intersection numbers on the moduli space of Higgs bundles. <i>Advances in Theoretical and Mathematical Physics</i>. 1998;2(5):1011-1040. doi:<a href=\"https://doi.org/10.4310/ATMP.1998.v2.n5.a3\">10.4310/ATMP.1998.v2.n5.a3</a>"},"title":"Vanishing of intersection numbers on the moduli space of Higgs bundles","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.","article_processing_charge":"No","publication_status":"published","publication":"Advances in Theoretical and Mathematical Physics","abstract":[{"lang":"eng","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. &quot;there are no topological L2 harmonic forms on M&quot;. 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."}],"date_created":"2018-12-11T11:52:06Z","arxiv":1,"date_updated":"2022-09-01T14:09:49Z","scopus_import":"1","main_file_link":[{"url":"http://arxiv.org/abs/math/9805071","open_access":"1"}],"user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","date_published":"1998-09-01T00:00:00Z","extern":"1","author":[{"first_name":"Tamas","last_name":"Hausel","full_name":"Hausel, Tamas","id":"4A0666D8-F248-11E8-B48F-1D18A9856A87"}],"oa_version":"Preprint","_id":"1450","publist_id":"5747","page":"1011 - 1040","article_type":"original","publication_identifier":{"issn":["1095-0761"]},"status":"public","intvolume":"         2","oa":1,"month":"09","year":"1998","day":"01","doi":"10.4310/ATMP.1998.v2.n5.a3","volume":2,"quality_controlled":"1"}