2014 Theses Doctoral
Three-Manifold Mutations Detected by Heegaard Floer Homology
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.
Files
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Clarkson_columbia_0054D_11918.pdf application/pdf 473 KB Download File
More About This Work
- Academic Units
- Mathematics
- Thesis Advisors
- Lipshitz, Robert
- Degree
- Ph.D., Columbia University
- Published Here
- July 7, 2014