A homotopy reciprocity law for ribbon disc complements
Cavagnaro, Catherine Elizabeth
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https://hdl.handle.net/2142/22924
Description
Title
A homotopy reciprocity law for ribbon disc complements
Author(s)
Cavagnaro, Catherine Elizabeth
Issue Date
1995
Doctoral Committee Chair(s)
Craggs, Robert F.
Department of Study
Mathematics
Discipline
Mathematics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Mathematics
Language
eng
Abstract
In this paper, we present two new spines for ribbon disc complements. We describe Craggs's 3-dimensional spine and introduce a 2-dimensional spine ${\cal W}\sp2$ which we show satisfies the homotopy reciprocity law. We demonstrate that the reciprocity property remains invariant under insertions and conjecture that the property is invariant under deletions. If this is the case, then the ribbon disc complement spines described here satisfy the reciprocity law and, hence, are Kervaire.
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