Heegaard Floer homology of some Mazur type manifolds
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- by Selman Akbulut and Çağri Karakurt PDF
- Proc. Amer. Math. Soc. 142 (2014), 4001-4013 Request permission
Abstract:
We show that an infinite family of contractible $4$-manifolds has the same boundary as a special type of plumbing. Consequently the Ozsváth–Szabó invariants can be calculated algorithmically. We run this algorithm for the first few members of the family and list the resulting Heegaard Floer homologies. We also show that the rank of the Heegaard Floer homology can get arbitrarily large values in this family by using its relation with the Casson invariant. For comparison, we list the ranks of Floer homologies of all the examples of Brieskorn spheres that are known to bound contractible manifolds.References
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Additional Information
- Selman Akbulut
- Affiliation: Department of Mathematics, Michigan State University, East Lansing, Michigan 48824
- MR Author ID: 23925
- Email: akbulut@math.msu.edu
- Çağri Karakurt
- Affiliation: Department of Mathematics, The University of Texas at Austin, 2515 Speedway, Stop C1200, Austin, Texas 78712
- Email: karakurt@math.utexas.edu
- Received by editor(s): April 28, 2012
- Received by editor(s) in revised form: September 13, 2012, and December 3, 2012
- Published electronically: July 17, 2014
- Additional Notes: The first named author is partially supported by NSF FRG grants DMS-1065879 and DMS-0905917.
The second named author is supported by a Simons fellowship and NSF FRG grant DMS-1065718. - Communicated by: Daniel Ruberman
- © Copyright 2014
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 142 (2014), 4001-4013
- MSC (2010): Primary 57R58, 57R65, 57R57
- DOI: https://doi.org/10.1090/S0002-9939-2014-12149-6
- MathSciNet review: 3251740