 
Summary: UNIVERSITY OF CALIFORNIA, SANTA BARBARA
BERKELEY · DAVIS · IRVINE · LOS ANGELES · MERCED · RIVERSIDE · SAN DIEGO · SAN FRANCISCO
CSANTA BARBARA · SANTA CRUZ
Geometry, Topology, and Physics Seminar
Manifold Pairings and
ThreeManifold Positivity
Mike Freedman (Microsoft Research)
Friday, October 27, 2006, 3:30 p.m.
Room 6635 South Hall
Abstract:
Gluing two manifolds along a common boundary so that the boundary disappears
is a fundamental operation of topology. In the spirit of physics we may consider
"superpositions", i.e., complex linear combinations, of nmanifolds bounding a fixed
(n1)manifold S. Two such superpositions may be glued along S to yield a
superposition of closed nmanifolds. It is known (work with: Wang, Slingerland,
Kitaev, and Walker and another study by Teichner and Kreck)) that in dimensions
n > 3 these pairings can have null vectors, v = 0 yet v, v = 0. Joint work with
Calegari and Walker shows that when n = 3 these pairings are positive (lack null
vectors). The proof is fun because it uses nearly everything we know about three
manifolds. In historical order: loop theorem/Dehn's lemma, prime decomposition,
