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On Configurations Of Spatial Planar Graphs

Author
Marshall, Andrew
Abstract
We investigate the homotopy type of a variety of families of configurations of graphs in R3 and S 3 . Preliminary results give that the linear configurations of the tetrahedral graph in R3 has the homotopy type of the double mapping cylinder SO(3)/A4 ← SO(3)/A3 [RIGHTWARDS ARROW] SO(3)/S3 , for An the alternating group and Sn the symmetric group. Two presentations and an action on the free group are given. This result is generalized to two families of configuration spaces of codimension 2 and 3 skeleta of simplices in Rn . The final segment is toward understanding the space of unknotted smooth embeddings of spatial planar graphs.
Date Issued
2014-08-18Subject
Configuration Spaces; Topological Graph Theory; Algebraic Topology
Committee Chair
Hatcher, Allen E
Committee Member
Riley, Timothy R.; Brown, Kenneth Stephen
Degree Discipline
Mathematics
Degree Name
Ph. D., Mathematics
Degree Level
Doctor of Philosophy
Type
dissertation or thesis