Back to Commutative Algebra Seminar: Fall 2018
Commutative Algebra Seminar
Date: Friday, Aug 31, 2018
Time: 2:30PM - 3:20PM
Location: LCB 215
Ben Briggs
University of Utah
Title |
Lusternik-Schnirelmann category in commutative algebra |
Abstract |
L-S category is a numerical invariant originating in differential geometry, which has since found an important place in rational homotopy theory. In the early 80s commutative algebraists and rational homotopy theorists began to uncover deep parallels between their disciplines, greatly enriching both sides. Constructions and theorems on one side were found to have “looking-glass” analogues on the other. For example, L-S category can be defined for local rings or homomorphisms, and this invariant has been used to prove important results in local commutative algebra. Nonetheless, L-S category has not been well studied in commutative algebra in the years since. I will talk about an attempt to develop some of the properties of this invariant. In particular, I’ll present a looking glass analogue of the mapping theorem, which is invaluable for computing L-S category in rational homotopy theory. I will also be very careful to explain any topology I might want to use. |
Commutative Algebra