2009 Cascade Topology Seminar

Start Date: 04/25/2009
End Date: 04/26/2009

Speaker(s):

Jose Maria Cantarero (UBC)

Dan Dugger (U.Oregon)

Chad Giusti (U.Oregon)

Veronique Godin (U.Calgary)

Laurent Meersseman (U.Bourgogne/PIMS)

Ron Stern (UC Irvine)

Gang Tian (Princeton University)

Troy Winfree (U.Washington)

Location:

University of British Columbia

Topic:

The Cascade Topology Seminar is a biennial gathering of topologists from the Pacific Northwest and Southwestern Canada.

Description:

Speaker: Daniel Dugger (U.Oregon)

Title: Motivic stable homotopy groups

Speaker: Chad Giusti (U.Oregon)

Title: Unstable Vassiliev theory

Speaker: Veronique Godin (U.Calgary)
Title: Relative invariant of string topology

Speaker: Jose Maria Cantarero (UBC)

Title: Twisted K-theory and Groupoids

Speaker: Laurent Meersseman (PIMS/U.Bourgogne)

Title : Complex Manifolds, Real Quadrics and Convex Polytopes

Abstract : This is a joint work with Frederic Bosio (Poitiers,
France).
We investigate the topology of a large class of non-Kaehler compact
complex manifolds called LV-M manifolds. These manifolds are
diffeomorphic to real quadrics in the complex space C^n of a special
form, so we forget about the complex structures and work with this
model. On the other hand, LV-M manifolds admit a smooth torus action
whose quotient is a simple convex polytope and can be seen as a smooth
realization of moment-angle manifolds.

In this talk, I will explain how complicated is the topology of LV-M
manifolds by making a reduction to combinatorics of convex polytopes.
In particular, I will give a combinatorial formula for the homology
with coefficients in Z of LV-M manifolds. This uses cohomological
results of Buchstaber and Panov. I will also resolve an associated
wall-crossing problem by studying a set of surgeries defined on simple
convex polytopes.

Finally, I will discuss some consequences for compact complex
manifolds. In particular, I will prove that there exist affine compact
complex manifolds (that is manifolds with an atlas whose changes of
charts are affine biholomorphisms of C^n) with arbitrary complicated
homology groups. This contrasts with the Kaehler case : affine Kaehler
compact complex manifolds are covered by a complex torus.

Speaker: Ronald J. Stern (UC Irvine)

Title: Finite group actions on smooth 4-manifolds

Abstract: We will outline the construction of infinite families
of smooth actions of finite cyclic groups on simply connected smooth
4-manifolds with nontrivial Seiberg-Witten invariants with the property
that the actions are equivariantly homeomorphic but not equivariantly
diffeomorphic. This is joint work with Ron Fintushel and Nathan
Sunukjian.

Speaker: Troy Winfree (U. Washington)

Title: Continuous homotopy fixed point spectra: finiteness properties and computations

Speaker: Gang Tian (Princeton University)

Title: Spaces with bounded Ricci curvature in dimension 4

Abstracts / Downloads / Reports:
Cascade_Topology_2009_Final_Report.pdf

Schedule:

Location: PIMS UBC--West Mall Annex Room 110

Saturday April 25

10:30 am Coffee & pastries

11:00 am Ron Stern (UC Irvine)

==lunch break==

1:30-1:55pm Troy Winfree (U.Washington)