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

- Series
- Geometry Topology Seminar
- Time
- Monday, March 29, 2021 - 14:00 for 1 hour (actually 50 minutes)
- Location
- ONLINE
- Speaker
- Yan Mary He – University of Toronto – yanmary.he@mail.utoronto.ca

The shift locus of (monic and centered) complex polynomials of degree *d* > 1 is 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.