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The theta invariant of homology 3-spheres


Speaker: Greg Kuperberg, UCD
Location: 693 Kerr
Start time: Wed, Apr 18 2001, 4:10PM

Abstract: Inspired by Witten's work on Chern-Simons topological quantum field theory, which was presaged by Albert Schwarz, Kontsevich defined a family of invariants of rational homology 3-spheres. Rational homology 3-sphere are in other words the closed, orientable 3-manifolds with vanishing first Betti number. The simplest of these invariants is called the theta invariant, because it corresponds to the Feynman diagram that looks a theta. The theta invariant has an interesting mathematical history: Calculations strongly supported the conjecture that it equals the celebrated Casson invariant. But for a long time there was a result in the literature, now retracted, that the theta invariant is trivial. I will define the theta invariant, and, if time permits, outline the argument due to Dylan Thurston and myself that it equals the Casson invariant.