November 15th, 2007
Ryan Budney (U Victoria)
Title: Embeddings of 3-manifolds in the 4-sphere from the point of view of the 11-tetrahedron census
Abstract: I will outline the problem of determining which 3-manifolds
embed in the 4-sphere. This will have essentially 3 parts:
- Known obstructions to a 3-manifold embedding in the 4-sphere such as torsion
linking forms, Alexander polynomials, the Rochlin invariant, the
Oszvath-Szabo d-invariant, Casson-Gordon invariants.
- Procedures for constructing embeddings
- Computations: Recent independent work of Matveev, Petronio and Burton has produced lists of all the 3-manifolds
(up to homeomorphism) that can be triangulated with 11 or less tetrahedra.
Computer implementation of known obstructions gives gives us a list of
all 3-manifolds which pass the tests (1) but for which we still, as of yet,
do not know if they embed in S^4. I will describe some characteristic
manifolds from this list.