Description
Algebra Seminar.
Speaker: Satya Mandal.
Affiliation: University of Kansas.
Date and Time: Thursday 16 May, 3:30 pm - 4:30 pm.
Venue: Ramanujan Hall, Department of Mathematics.
Title: Homotopy obstructions for Projective Modules.
Abstract: The Theory for vector bundles in topology shaped the research in
projective modules in algebra, consistently. This includes Obstruction
Theory. The
algebra has always been trying to catch up. To an extent, this fact
remained under
appreciated.
For an affine scheme $X=\spec{A}$, and a projective $A$-module $P$, our
objective
would be to define an obstruction class $\varepsilon(P)$ in a suitable
obstruction
house (preferably a group), so the triviality of $\varepsilon(P)$ would
imply $P
\equiv Q \oplus A$. One would further hope the obstruction house is an
invariant of
$X$; not of $P$. We would report on what is doable. We detect splitting $P
\equiv Q
\oplus A$ by homotopy.