UCSD Topology/Geometry Seminars, Fall 2002
UCSD Topology/Geometry Seminars, Fall 2002
Math 292A, Fall 2002, Fridays 4:00-5:30 in room 7218.
Organisers: Justin Roberts, Peter Teichner
The following is a provisional list of speakers:
September 27: Shelly Harvey (UCSD) Higher-order 3-manifold
invariants and their applications; Part I
We define an infinite sequence of new invariants, delta_n, of a group
G that measure the size of the successive quotients of the derived
series of G. In the case that G is the fundamental group of a
3-manifold, we obtain new 3-manifold invariants. These invariants are
closely related to the topology of the 3-manifold. They give lower
bounds for the Thurston norm which provide better estimates than the
bound established by McMullen using the Alexander norm. We also show
that the delta_n give obstructions to a 3-manifold fibering over S^1
and to a 3-manifold being Seifert fibered. Moreover, we show that the
delta_n give computable algebraic obstructions to a 4-manifold of the
form X x S^1 admitting a symplectic structure even when the
obstructions given by the Seiberg-Witten invariants fail. There are
also applications to the minimal ropelength of knots and links in S^3.
In addition, we discuss the applications to the cut number of a
3-manifold (this is also known as the corank of the fundamental group
of the 3-manifold).
October 4: Shelly Harvey (UCSD) Part II
October 11: Shelly Harvey (UCSD) Part III
October 18: Mark Gross (UCSD) Affine manifolds and
Calabi-Yau manifolds
October 25: Ko Honda (USC) Knots and contact geometry
In this talk I will present joint work with John Etnyre on
classification and structure theorems for Legendrian knots in the
standard contact 3-space. I will describe some of the unexpected
phenomena that arise along the way.
November 1: Rob Kirby (UC Berkeley) Foliations and almost
complex structures on 4-manifolds
November 7: Ilia Zharkov (Duke) Integral affine structures on
Calabi-Yau degenerations
November 8: Ken Bromberg (Caltech)
Projective structures with degenerate holonomy and the Bers density
conjecture
November 15: Ralph Cohen (Stanford) Loop spaces and string
homology
November 22: Ted Stanford (NMSU) Vassiliev invariants and
double-delta moves
December 6: John Baez (UC Riverside) Vector products in dimension
0,1,3,7
justin@math.ucsd.edu
Image of (-2,3,-5) pretzel knot from Rob Scharein's
KnotPlot Site.
