Equivariant framings, lens spaces and Contact structures

2001/03/27 by Siddhartha Gadgil, Gadgil, Siddhartha
Mathematics · #57M27 #57M60 #FOS: Mathematics #Geometric Topology (math.GT) #math.GT #msc:57M27 #msc:57M60

paper · pdf · doi:10.48550/arxiv.math/0103183

10 pages, to appear in the Pacific Journal of Mathematics

arxiv created 2001/12/24 · arxiv updated 2009/11/30

Abstract

We construct a simple topological invariant of certain 3-manifolds, including quotients of the 3-sphere by finite groups, based on the fact that the tangent bundle of an orientable 3-manifold is trivialisable. This invariant is strong enough to yield the classification of lens spaces of odd, prime order. We also use properties of this invariant to show that there is an oriented 3-manifold with no universally tight contact structure. We generalise and sharpen this invariant to an invariant of a finite covering of a 3-manifold.

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