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Orbifold Morse Functions and Associated Handle Decompositions

Sean Corrigan, SLU

  • PhD Oral Exam
  • Geometry/ Topology Seminar
  • Topology Seminar
When Tue, Nov 17, 2015
from 11:00 AM to 12:00 PM
Where 323 Ritter Hall
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Morse theory has been an indispensable tool in the study of manifolds, but its generalization to orbifolds has gone mostly undeveloped until the past decade. I will discuss the basic definitions surrounding Morse theory for orbifolds (particularly the index of an orbifold critical point)  and show some examples which convey the correspondence between orbifold Morse functions and orbifold-handle decompositions.

A particular emphasis will be placed on oriented 3-dimensional orbifolds, where we will see a list of 20 distinct handle-types. I will provide a Morse function for an orbifold-three-sphere whose singular locus is a set of Borromean rings, and we will look at the corresponding handle decomposition. This example has the property that the singular orbifold-handle attachments will affect the orbifold structure without altering the topology of the underlying space.

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