The Århus Integral of Rational Homology 3-Spheres I: A Highly Non Trivial Flat Connection on S³ (2002)
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@MISC{Bar-Natan02theårhus,
author = {Dror Bar-Natan and Stavros Garoufalidis and Lev Rozansky and Dylan P. Thurston},
title = {The Århus Integral of Rational Homology 3-Spheres I: A Highly Non Trivial Flat Connection on S³},
year = {2002}
}
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Abstract
Path integrals do not really exist, but it is very useful to dream that they do and figure out the consequences. Apart from describing much of the physical world as we now know it, these dreams also lead to some highly non-trivial mathematical theorems and theories. We argue that even though non-trivial at connections on S³ do not really exist, it is beneficial to dream that one exists (and, in fact, that it comes from the non-existent Chern-Simons path integral). Dreaming the right way, we are led to a rigorous construction of a universal finite-type invariant of rational homology spheres. We show that this invariant is equal (up to a normalization) to the LMO (Le-Murakami-Ohtsuki, [LMO]) invariant and that it recovers the Rozansky and Ohtsuki invariants. This is part I of a 4...
