Invariants of knots and 3-manifold

Lecture course with Wolfgang Lück, Summer 2018

Tu. 15 - 17h, Th. 13 - 15h, MPIM Lecture Hall

Peter:

May 3: How to see low-dimensional manifolds, up to dimension 4

May 8: Classification of compact manifolds up to dimension 3

May 15: 4-manifolds and Kirby calculus

May 17: Reading off invariants from handle decompositions

June 5: Intersection forms in algebra and topology

June 21: Signature invariants

June 26: C*- and von Neumann algebras

June 28: L^2 signatures of knots

July 12: Casson-Gordon invariants via L^2-signatures

July 17: Filtrations of the knot concordance group

July 19: Some open problems in low-dimensional topology

Wolfgang:

April 10 & 12: Survey on 3-manifolds

April 12 & 17: Cobordism theory and the s-cobordism theorem

April 17 & 19: Introduction to surgery theory

April 24 & 26: L^2-Betti numbers

May 29 & June 12: Classical torsion and L^2-torsion

June 14 & 19: L^2-invariants and 3-manifolds

July 10: The stable Cannon conjecture

Guest lectures:

June 7: The Alexander polynomial, Aru Ray

July 3: Fibred knots, Filip Misev

July 5: Gauge theory and applications to knot concordance, Paolo Aceto