## 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