On algebraic vector bundles over configuration spaces

Igor Kříž

University of Michigan

Abstract

A commutative ring R is said to have the Quillen-Suslin property if every finitely generated projective module over R is free. A famous theorem of Quillen and Suslin (solving a question of Serre) states that the ring of polynomials in n variables over a field is Quillen-Suslin. The result was later generalized by Gubeladze, and there are also effective algorithmic versions, which have applications in signal processing. In this talk, I will show that the ring polynomial ring in n variables x_1,...,x_n with all x_i-x_j with i,j different inverted is Quillen-Suslin. This result has an interesting geometric interpretation relevant in mathematical physics. An algorithmic solution remains an interesting open problem.