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Three-Manifold Mutations Detected by Heegaard Floer Homology

Corrin Clarkson

Title:
Three-Manifold Mutations Detected by Heegaard Floer Homology
Author(s):
Clarkson, Corrin
Thesis Advisor(s):
Lipshitz, Robert
Date:
Type:
Dissertations
Department(s):
Mathematics
Persistent URL:
Notes:
Ph.D., Columbia University.
Abstract:
Given a self-diffeomorphism h of a closed, orientable surface S with genus greater than one and an embedding f of S into a three-manifold 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 three-manifold M such that the rank of the non-torsion summands of HF-hat 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 genus-two hyperelliptic involution, then there exists an embedding of S into a three-manifold M such that the total rank of HF-hat of M differs from that of its mutant.
Subject(s):
Mathematics
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840
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Suggested Citation:
Corrin Clarkson, , Three-Manifold Mutations Detected by Heegaard Floer Homology, Columbia University Academic Commons, .

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