Topology Seminar

Seminars During Academic Year 2001-02

Fall 2001

Thursday October 25, 2001 in RH104

Alejandro Adem, Representations and K-theory of the Braid Groups

Thursday November 15, 2001 in Rawles Hall

Bob Oliver, Actions of finite groups on acyclic 2-complexes

Thursday November 29, 2001 in Rawles Hall

Jim McClure, Operads and cosimplicial spaces

Spring 2002

Wednesday January 9, 2002 in Rawles Hall

Chuck Livingston, Concordance Genus of Knots

The concordance genus of a knot K is the minimum genus among all knots concordant to K. I will discuss relations between the concordance genus and classically studied knot invariants. The computation of the concordance genus for low crossing-number knots will also be described.

Wednesday January 16, 2002 in Rawles Hall 104

Jan Jaworowski, Periodic maps on vector space bundles

Wednesday January 23, 2002 in RH 104

Charles Delman, Laminar 3-manifolds: an introduction

Wednesday January 30, 2002 in RH 104

Charles Delman, Laminar 3-manifolds

Wednesday February 6, 2002 in RH 104

Scott Baldridge, Classification of symplectic 4-manifolds which admit circle actions with fixed points

Wednesday February 13, 2002 in RH 104

Paul Kirk, The Atiyah-Patodi-Singer rho invariant for manifolds wth boundary

Wednesday February 20, 2002 in RH 104

Zhenghan Wang, Curves on surfaces and topological field theories

Wednesday February 27, 2002 in Rawles Hall

Ayelet Lindenstrauss, The Hochschild homology of fatpoints

I will talk about a calculation of the Hochschild homology of the ring k[x_1,...,x_n]/{frak M}^a, where M is the ideal (x_1,...,x_n) and k is a characteristic zero field. Using simplicial methods, this Hochshild homology can be described in terms of the homology of tori relative to their “a-fat” diagonals (all points in the torus, exhibited as a product of circles, where a or more coordinates are the same).

Wednesday March 6, 2002 in RH 104

Charles Livingston, Knotting Contractible 4-manifolds in R^4

Wednesday March 27, 2002 in RH 104

Dusan Repovs, New Results on 2-polyhedra in 3- and 4-manifolds

We shall present a very broad survey of results, starting from the mid 1960's, addressed at a very general audience, concerning the geometric topology of polyhedra and the main applications. Here are the key topics to be covered in the talk: 2-dimensional PL topology: We shall consider the problem of resolving arbitrary 2-polyhedra by fake surfaces and its application to getting a reduction of the classical Whitehead asphericity conjecture to the case of special polyhedra (Casler, Ikeda, Piergallini-Matveev, Wright, Hog-Angeloni-Metzler, Repovs-Skopenkov). 3-dimensional PL topology. We shall study spines of topological 3-manifolds and an interesting application of the classical knot theory in producing nonhomeomorphic 3-manifolds with equivalent spines (Mitchell-Przytycki-Repovs, Cavicchioli-Lickorish-Repovs, Glock-Hog-Angeloni) as well as problems of thickenings (Brodsky-Repovs-Skopenkov). 4-dimensional PL topology. We shall investigate embeddings of 2-polyhedra into topological 4-manifolds and an interesting application of the classical Bing shrinking techniques to the problem of different regular neighborhoods of codimension 2 embeddings (Geoghegan-Mihalik, Lasheras, Salihov, Oniscenko-Repovs-Skopenkov, Bestvina-Daverman-Venema-Walsh). We shall also list several open problems and open conjectures from this and related areas of geometric topology.

Wednesday April 3, 2002 in RH 104

Jim Davis, Gromov-Lawson-Rosenberg Conjecture for Cocompact Fuchsian Groups

We give nasc for a closed manifold of dimension greater than for 4 whose fundamental group is cocompact Fuchsian to admit a metric of positive scalar curvature.

Wednesday April 10, 2002 in RH 104

Diarmuid Crowley, Quadratic Z modules, Kreck monoids and the classification of simply

Wednesday April 17, 2002 in RH 104

Ben Himpel, Casson's invariant and gauge theory

Wednesday April 24, 2002 in RH 104

Paul Kirk, SU(3) Casson Invariant

Wednesday May 15, 2002 in Rawles Hall 104

Scott Carter, Dynamical quandle cocycles and twist-spun knots.

There has been a burst of activity recently in quandle theory. Andruskiewitsch and Grana (among others) are developing quandle cohomology is relation to classifying certain pointed Hopf Algebras. They have defined a general quandle cohomology theory that encompasses those given by Fenn and Rourke and generalizations by me and my collaborators (CJKLS) and Ohtsuki. One notion of Andruskiewtsch and Grana that is particularly helpful is that of a dynamical 2-cocycle. Angela Harris (who is currently a master's degree student at University of South Alabma), Masahico Saito and I are looking into the following. Starting from a Fox coloring of a classical knot we indicate how to extend the coloring to a coloring using a dynamical 2-cocycle. We then use this extension to give colorings of various twist-spuns of the original knot. Our purpose is to generalize the results of Shima and Satoh on the minimal number of triple points for the 2 and 3 twist-spin trefoils. The talk can be self-contained at an introductory level if graduate students are present.