The N+1st Southern California Topology Conference

Saturday May 22nd, 2004

Map of campus is available here

Parking:

in the faculty parking lot across California from Sloan, bordering the excavation. (Note there is also parking at the back of the lot, behind the tennis courts). Parking is also available on California.

Coffee and donuts available outside 151 Sloan, 10-10:30 am

Schedule of talks:

Speaker	Time	Room	Title
Michael Handel, CUNY	10:30-11:30 am	151 Sloan	Distortion elements in group actions on surfaces
Peter Teichner, UCSD	1:30-2:30 pm	151 Sloan	New obstructions for embedding 2-spheres into 4-manifolds
Elizabeth Klodginski, UC Davis	2:45-3:45 pm	151 Sloan	Geometry of essential surfaces in 3-manifolds fibering over the circle
Michael Hutchings, UC Berkeley	4-5 pm	151 Sloan	Examples of embedded contact homology

Abstracts of talks:

Michael Handel. Title: Distortion elements in group actions on surfaces
Abstract: If G is a finitely generated group with generators {g₁, . . . ,g_j} then an infinite order element f in G is a distortion element of G provided

liminf |fⁿ|/n = 0 where |fⁿ| is the word length of fⁿ in the generators. Let S be a closed orientable surface and let Diff(S)₀ denote the identity component of the group of C¹ diffeomorphisms of S. Our main result shows that if S has genus at least two and if f is a distortion element in some finitely generated subgroup of Diff(S)₀, then the support of m is a subset of Fix(f) for every f-invariant Borel probability measure m. Related results are proved for S homeomorphic to a torus or a sphere. For m a Borel probability measure on S, denote the group of C¹ diffeomorphisms that preserve m by Diff_m(S)₀. We give several applications of our main result showing that certain groups, including a large class of higher rank lattices, admit no homomorphisms to Diff_m(S)₀ with infinite image.

Peter Teichner. Title: New obstructions for embedding 2-spheres into 4-manifolds
Abstract: In joint work with Rob Schneiderman, we have developed a new obstruction theory for the embedding problem for 2-spheres in 4-manifolds. It is given in terms of the intersection theory of Whitney towers, immersed in the 4-manifold, and it is related to Milnor invariants and the Kontsevich integral in the easiest cases (where the 4-manifold is given by attaching 2-handles to a link in the 3-sphere). As a consequence, we give an intersection theoretic explanation of the Milnor invariants, and we relate them to the existence of embedded gropes in the 4-ball.

Elizabeth Klodginski. Title: Geometry of essential surfaces in 3-manifolds fibering over the circle
Abstract: Given a surface bundle over the circle M, we find a condition of the monodromy characterizing when certain immersed essential surfaces have the 1-line property. As a consequence, when M is hyperbolic, the surfaces are not homotopic to a totally geodesic surface. Furthermore, they cannot be the canonical surface of a non-positively curved cubed structure on M.

Michael Hutchings. Title: Examples of embedded contact homology
Abstract: Embedded contact homology is an invariant of contact 3-manifolds which counts certain embedded pseudoholomorphic curves in the symplectization. Although much remains to be done to develop this theory in general, we can explicitly compute it for the example of the three-torus, in terms of some nontrivial combinatorics involving convex polygons in the plane with vertices at lattice points. We obtain evidence for the possibly surprising conjecture that embedded contact homology is isomorphic to a version of Seiberg-Witten Floer homology, and in particular is independent of the contact structure. (joint work with Michael Sullivan)

Recreational activities:

Dinner at some fine local Pasadena restaurant.