Topology Seminar

Chris Davis
Concordance and homotopy for knots in homology spheres

Any knot in $S^3$ may be reduced to a slice knot by  crossing changes, in other words a homootpy.  Indeed, this slice knot can be taken to be the unknot. During this talk I shall ask when the same holds for knots in a homology sphere.  I will prove that that a knot in a homology sphere is nullhomotopic in a smooth homology ball if and only if that knot is smoothly concordant to a knot which is homotopic to a smoothly slice knot.  As a consequence, we prove that the equivalence relation on knots in homology spheres given by cobounding immersed annuli in a homology cobordism is generated by concordance in homology cobordisms together with homotopy in a homology sphere.  

Event Date: 
December 5, 2019 - 2:00pm to 3:00pm
217 MLH
Calendar Category: 
Seminar Category: 
Geometry and Topology