Topology of the Shift Locus via Big Mapping Class Groups by Yan Mary He

Geometry Topology Seminar
Monday, March 29, 2021 - 2:00pm for 1 hour (actually 50 minutes)
Yan Mary He – University of Toronto – yanmary.he@mail.utoronto.ca
Roberta Shapiro

The shift locus of (monic and centered) complex polynomials of degreeĀ d > 1 isĀ the set of polynomials whose filled-in Julia set contains no critical points. Traversing a loop in the shift locus gives rise to a holomorphic motion of Cantor Julia sets, which can be extended to a homeomorphism of the plane minus a Cantor set up to isotopy. Therefore there is a well-defined monodromy representation from the fundamental group of the shift locus to the mapping class group of the plane minus a Cantor set. In this talk, I will discuss the image and the kernel of this map as well as a combinatorial model for the shift locus. This is joint work with J. Bavard, D. Calegari, S. Koch and A. Walker.