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Heegaard Floer homology of some Mazur type manifolds

Authors: Selman Akbulut and Çağri Karakurt
Journal: Proc. Amer. Math. Soc. 142 (2014), 4001-4013
MSC (2010): Primary 57R58, 57R65, 57R57
Published electronically: July 17, 2014
MathSciNet review: 3251740
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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.

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Additional Information

Selman Akbulut
Affiliation: Department of Mathematics, Michigan State University, East Lansing, Michigan 48824

Çağri Karakurt
Affiliation: Department of Mathematics, The University of Texas at Austin, 2515 Speedway, Stop C1200, Austin, Texas 78712

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
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.