ThreeManifold Mutations Detected by Heegaard Floer Homology
 Title:
 ThreeManifold Mutations Detected by Heegaard Floer Homology
 Author(s):
 Clarkson, Corrin
 Thesis Advisor(s):
 Lipshitz, Robert
 Date:
 2014
 Type:
 Dissertations
 Department(s):
 Mathematics
 Persistent URL:
 http://dx.doi.org/10.7916/D8GF0RNG
 Notes:
 Ph.D., Columbia University.
 Abstract:
 Given a selfdiffeomorphism h of a closed, orientable surface S with genus greater than one and an embedding f of S into a threemanifold M, we construct a mutant manifold by cutting M along f(S) and regluing by h. We will consider whether there exist nontrivial gluings such that for any embedding, the manifold M and its mutant have isomorphic Heegaard Floer homology. In particular, we will demonstrate that if h is not isotopic to the identity map, then there exists an embedding of S into a threemanifold M such that the rank of the nontorsion summands of HFhat of M differs from that of its mutant. We will also show that if the gluing map is isotopic to neither the identity nor the genustwo hyperelliptic involution, then there exists an embedding of S into a threemanifold M such that the total rank of HFhat of M differs from that of its mutant.
 Subject(s):
 Mathematics
 Item views
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 Suggested Citation:
 Corrin Clarkson, 2014, ThreeManifold Mutations Detected by Heegaard Floer Homology, Columbia University Academic Commons, http://dx.doi.org/10.7916/D8GF0RNG.