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.

## Subjects

## Files

- Clarkson_columbia_0054D_11918.pdf binary/octet-stream 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