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Matroid Relationships: Matroids for Algebraic Topology
Estill, Charles

2013, Doctor of Philosophy, Ohio State University, Mathematics.
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.
Sergei Chmutov (Advisor)
Thomas Kerler (Committee Member)
Matthew Kahle (Committee Member)
Manouchehri Azita (Committee Member)
92 p.

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Estill, Charles. "Matroid Relationships: Matroids for Algebraic Topology." Electronic Thesis or Dissertation. Ohio State University, 2013. OhioLINK Electronic Theses and Dissertations Center. 25 Sep 2017.

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Estill, Charles "Matroid Relationships: Matroids for Algebraic Topology." Electronic Thesis or Dissertation. Ohio State University, 2013. https://etd.ohiolink.edu/

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