Dissertation/Thesis Abstract

Relative Khovanov-Jacobsson classes for spanning surfaces
by Swann, Jonah, Ph.D., Bryn Mawr College, 2010, 119; 3402691
Abstract (Summary)

We define the Khovanov-Jacobsson class for a properly embedded surface in the 4-ball, an element of the Khovanov homology of its boundary link in the 3-sphere. We then develop general non-triviality criteria for Khovanov homology classes, and use these to distinguish the Khovanov-Jacobsson classes of various families of surfaces. Among these are pairs of distinct slice disks for pretzel knots, and the first known examples of pairs of Seifert surfaces of equal genus for links in the 3-sphere that remain distinct when pushed into the 4-ball.

Indexing (document details)
Advisor: Melvin, Paul
Commitee: Cheng, Leslie, Donnay, Victor, Grundman, Helen, Schultz, Michael
School: Bryn Mawr College
Department: Mathematics
School Location: United States -- Pennsylvania
Source: DAI-B 71/05, Dissertation Abstracts International
Subjects: Mathematics
Keywords: Embedded surfaces, Khovanov-Jacobsson classes, Spanning surfaces
Publication Number: 3402691
ISBN: 978-1-109-75044-7
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