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Vertex Groups of Locally Oriented Orbifolds, Orbifold Cobordism, and a Differential Graded Algebra

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Kimberly Druschel, Saint Louis University

What
  • Topology Seminar
When Fri, Nov 30, 2012
from 11:00 AM to 11:50 AM
Where Ritter Hall 316
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Oriented orbifold cobordism with rational coefficients is fairly well understood-invariants and generators are known. One step in studying the actual orbifold cobordism ring involves determining which combinations of finite, degree n subgroups of SO(n) can occur in an oriented or locally oriented n dimensional orbifold. This was key in calculations up through dimension four.

 

I'll give a brief overview of orbifold cobordism with examples and pictures. I'll then focus on the above question by providing a first obstruction to a given set of such subgroups occurring in some oriented n-orbifold. This is the only obstruction in dimensions two through four. From this we build a differential d associated with finite degree n subgroups of SO(n), with n varying, and hence obtain a homology.

 

I'll show how this homology relates to orbifold cobordism and compute d for many cases, including dimensions less than or equal to four and also direct sums and products. Additionally, if an oriented degree n group G admits an orientation reversing linear automorphism u, we construct a semidirect product of G by (u,-1) in degree n+1. I'll present equations for calculating d of this semidirect product.

 
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