Lipshitz, Robert and Manolescu, Ciprian and Wang, Jiajun (2008) Combinatorial cobordism maps in hat Heegaard Floer theory. Duke Mathematical Journal, 145 (2). pp. 207-247. ISSN 0012-7094. doi:10.1215/00127094-2008-050. https://resolver.caltech.edu/CaltechAUTHORS:20090721-074520260
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Abstract
In a previous article, Sarkar and Wang [15] gave a combinatorial description of the hat version of Heegaard Floer homology for three-manifolds. Given a cobordism between two connected three-manifolds, there is an induced map between their Heegaard Floer homologies. Assume that the first homology group of each boundary component surjects onto the first homology group of the cobordism (modulo torsion). Under this assumption, we present a procedure for finding the rank of the induced Heegaard Floer map combinatorially, in the hat version.
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| Additional Information: | © 2008 Duke University Press. Received 15 December 2006. Revision received 30 January 2008. We thank Peter Ozsváth and Zoltán Szabό for helpful conversations and encouragement. In particular, several key ideas in the proof were suggested to us by Ozsváth. This work was done while Jiajun Wang was an exchange graduate student at Columbia University; he is grateful to that university’s mathematics department for its hospitality. He also thanks his advisors, Robion Kirby and Peter Ozsváth, for their continuous guidance and support. Finally, we thank the referees for many helpful comments, particularly for finding a critical error in Section 4 of a previous version of this article. Lipshitz’s work partially supported by a National Science Foundation Mathematical Sciences Postdoctoral Research Fellowship. Manolescu's work partially supported by a Clay Research Fellowship. Wang’s work partially supported by National Science Foundation Holomorphic Curves Focused Research Group grant DMS-0244663. 2000 Mathematics Subject Classification. Primary 57R58; Secondary 57R56. | |||||||||
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| Issue or Number: | 2 | |||||||||
| DOI: | 10.1215/00127094-2008-050 | |||||||||
| Record Number: | CaltechAUTHORS:20090721-074520260 | |||||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20090721-074520260 | |||||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | |||||||||
| ID Code: | 14622 | |||||||||
| Collection: | CaltechAUTHORS | |||||||||
| Deposited By: | Ruth Sustaita | |||||||||
| Deposited On: | 27 Jul 2009 18:17 | |||||||||
| Last Modified: | 08 Nov 2021 23:13 |
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