Three-Manifold Mutations Detected by Heegaard Floer Homology
By: Corrin Clarkson
Publisher: [publisher not identified]
Published: 2014
Place of publication: [New York, N.Y.?]
Language: eng
Description: 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.
Notes: Department: Mathematics.

Thesis advisor: Robert Lipshitz.

Thesis (Ph.D.)--Columbia University, 2014.