Spring 2015

Time/Location: Th 1:00-1:50, Carney 309

Description: We will explore some of the topics discussed in this blog post of Danny Calegari based on some talks of Marty Scharlemann: in particular, our goal will be to understand how the smooth 4D Schoenflies conjecture is related to a generalized version of property R (as well as other 3- and 4-dimensional questions). Along the way, we will survey what is known and discuss some classical and modern techniques one might bring to bear on these questions.

Some references (will be updated/organized as the semester progresses):

• Robert Gompf and András Stipsicz, 4-manifolds and Kirby calculus

• Alexandru Scorpan, Wild world of 4-manifolds

• Moskovich's blog post on property nR and slice-ribbon conjecture

• Martin Scharlemann, Generalized property R and the Schoenflies conjecture

• Robert Gompf, Martin Scharlemann, and Abigail Thompson, Fibered knots and potential counterexamples to the property 2R and slice-ribbon conjectures

• Martin Scharlemann, Proposed property 2R counterexamples classified

• Martin Scharlemann, On-line talk

• Ian Agol and Michael Freedman, Simplifying 3-manifolds in R^4

• David Gabai, Foliations and the topology of 3-manifolds III

• Math overflow discussion of well-definedness of connected sum in topological category