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osu1338251228.pdf (2.15 MB)
ETD Abstract Container
Abstract Header
Comparing Invariants of 3-Manifolds Derived from Hopf Algebras
Author Info
Sequin, Matthew James
Permalink:
http://rave.ohiolink.edu/etdc/view?acc_num=osu1338251228
Abstract Details
Year and Degree
2012, Doctor of Philosophy, Ohio State University, Mathematics.
Abstract
This paper will compare two different quantum 3-manifold invariants, both of which are given using a finite dimensional Hopf Algebra
H
. One is the Hennings invariant, given by an algorithm involving the link surgery presentation of a 3-manifold and the Drinfeld double
D(H)
; the other is the Kuperberg invariant, which is computed using a Heegaard diagram of the 3-manifold and the same
H
. We show that when
H
is semi-simple, these two invariants are equal. The proof is entirely in Hopf algebraic terms and does not rely on the representation theory of
H
or general results involving categorical invariants.
Committee
Thomas Kerler (Advisor)
Zbigniew Fiedorowicz (Committee Member)
Nathan Broaddus (Committee Member)
Pages
106 p.
Subject Headings
Mathematics
Keywords
Hennings Invariant
;
Kuperberg Invariant
;
Hopf algebras
;
Quantum invariants
;
3-manifolds
;
Link Invariants
Recommended Citations
Refworks
EndNote
RIS
Mendeley
Citations
Sequin, M. J. (2012).
Comparing Invariants of 3-Manifolds Derived from Hopf Algebras
[Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1338251228
APA Style (7th edition)
Sequin, Matthew.
Comparing Invariants of 3-Manifolds Derived from Hopf Algebras.
2012. Ohio State University, Doctoral dissertation.
OhioLINK Electronic Theses and Dissertations Center
, http://rave.ohiolink.edu/etdc/view?acc_num=osu1338251228.
MLA Style (8th edition)
Sequin, Matthew. "Comparing Invariants of 3-Manifolds Derived from Hopf Algebras." Doctoral dissertation, Ohio State University, 2012. http://rave.ohiolink.edu/etdc/view?acc_num=osu1338251228
Chicago Manual of Style (17th edition)
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Document number:
osu1338251228
Download Count:
870
Copyright Info
© 2012, all rights reserved.
This open access ETD is published by The Ohio State University and OhioLINK.