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.
Academic Commons
Clarkson, Corrin
Author
Lipshitz, Robert
Thesis advisor
Columbia University. Mathematics
Originator
Theses
English
Mathematics
text
2014
eng
2017-06-08T20:11:41Z
2017-11-10T08:32:20Z
Ph.D.
2
Mathematics
Columbia University
10.7916/D8GF0RNG