UCSD Topology/Geometry Seminars, Fall 2003
UCSD Topology/Geometry Seminars, Fall 2003
Fridays 4:150-5:30 in room 7218.
Organisers: Justin Roberts, Peter Teichner
October 10: Tom Fleming (UCSD) Instrinsically knotted
graphs
October 17: Peter Teichner (UCSD) n-complexes in 2n-space:
Kuratowski, van Kampen, Whitney
October 24: Peter Teichner (UCSD) Thom's embedding theory
November 7: Peter Teichner (UCSD) n-complexes in 2n-space:
Kuratowski, van Kampen, Whitney II
November 14: Thomas Kerler (Ohio State)
TQFT's in Dimension 2+1 over the Cyclotomic Integers.
A Topological Quantum Field Theory (TQFT) is a functorial extension of
invariants of 3-manifolds to manifolds with boundaries. They are thus
highly structured and imply, for example, nontrivial representations
of the mapping class groups. A large family of such TQFT's is given by
the Witten-Reshetikhin-Turaev TQFT's. Assuming a mild modification of
the TQFT axioms it is possible to define them over the cyclotomic
integers (rather than just the complex numbers). The rich ideal
structure of this ring combined with the modified functoriality yields
a new and quite subtle tool to investigate various properties of the
mapping class groups, specific 3-manifolds, and some of their
classical invariants. In the talk I will give several examples of such
applications.
justin@math.ucsd.edu
Image of (-2,3,-5) pretzel knot from Rob Scharein's
KnotPlot Site.
