|Name||Jae Choon Cha|
|Time||Jan 9 11:10~12:00|
|Title||An introduction to $L^2$-invariants I|
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.