Name Jae Choon Cha POSTECH Tutorial Jan 11 11:10~12:00 E11-304 An 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. 304-1-11/2012-01_eas-L2-invariants-3.pdf