NameJae Choon Cha
Talk typeTutorial
TimeJan 11 11:10~12:00
TitleAn introduction to $L^2$-invariants III
In this series of lectures we introduce $L^2$-Betti numbers and $L^2$-signatures of manifolds and knots. We introduce the essentials of an algebraic formulation of the $L^2$-dimension theory, which is originally due to Wolfgang Lueck. Compared with the analytic approach, this is a flexible and easy-to-use setup that enables us to use standard techniques familiar to topologists. We discuss $L^2$-signatures and an Atiyah-type theorem for topological manifolds following the approach of Shmuel Weinberger. Some recent applications to knots are also introduced. Our treatment will be as elementary as possible, based on a minimal collection of analytic facts from graduate level functional analysis.