## 2009 Topology Seminar - 06

- Date: 03/04/2009

Lecturer(s):
Kee Yuen Lam (UBC)

Location:

University of British Columbia

Topic:

A synthesis of results on the geometric dimension problem

Description:

Consider a vector bundle E of rank k over a finite CW complex

X. Assume k>dimX for simplicity. If E is not trivial, then it will

contain various trivial sub-bundles of maximal rank r. The geometric

dimension of E is simply defined to be gd(E)=k-r. It provides a (crude)

measure of E's deviation from triviality.

In this talk I'll present some new observations concerning gd(E) when X

is a sphere or projective space. These will culminate in a new proof

that for X=S^8m+1 or S^8m+2, gd(E) is always equal to 6. [Joint work

with D. Randall]

Schedule:

3:00pm-4:00pm, WMAX 110