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estill-dissertation.pdf (609.33 KB)
ETD Abstract Container
Abstract Header
Matroid Relationships: Matroids for Algebraic Topology
Author Info
Estill, Charles
Permalink:
http://rave.ohiolink.edu/etdc/view?acc_num=osu1366301251
Abstract Details
Year and Degree
2013, Doctor of Philosophy, Ohio State University, Mathematics.
Abstract
In a paper written in 2001 we found a relationship between two polynomials cellularly embedded in a surface, the Krushkal polynomial, based on the Tutte polynomial of a graph and using data from the algebraic topology of the graph and the surface, and the Las Vergnas polynomial for the matroid perspective from the bond matroid of the dual graph to the circuit matroid of the graph, B(G*) -> C(G). With Vyacheslav Krushkal having (with D. Renardy) expanded his polynomial to the nth dimension of a simplicial or CW decomposition of a 2n-dimensional manifold, a matroid perspective was found whose Las Vergnas polynomial would play a similar role to that in the 2-dimensional case. We hope that these matroids and the perspective will prove useful in the study of complexes.
Committee
Sergei Chmutov (Advisor)
Thomas Kerler (Committee Member)
Matthew Kahle (Committee Member)
Manouchehri Azita (Committee Member)
Pages
92 p.
Subject Headings
Mathematics
Keywords
Matroid
;
Algebraic Topology
;
Simplicial complex
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Citations
Estill, C. (2013).
Matroid Relationships: Matroids for Algebraic Topology
[Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1366301251
APA Style (7th edition)
Estill, Charles.
Matroid Relationships: Matroids for Algebraic Topology.
2013. Ohio State University, Doctoral dissertation.
OhioLINK Electronic Theses and Dissertations Center
, http://rave.ohiolink.edu/etdc/view?acc_num=osu1366301251.
MLA Style (8th edition)
Estill, Charles. "Matroid Relationships: Matroids for Algebraic Topology." Doctoral dissertation, Ohio State University, 2013. http://rave.ohiolink.edu/etdc/view?acc_num=osu1366301251
Chicago Manual of Style (17th edition)
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Document number:
osu1366301251
Download Count:
2,012
Copyright Info
© 2013, all rights reserved.
This open access ETD is published by The Ohio State University and OhioLINK.