Common fixed points of commuting homeomorphisms of S^2.

Series
Geometry Topology Student Seminar
Time
Wednesday, March 1, 2023 - 2:00pm for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Cindy Tan – University of Chicago – cindy@math.uchicago.eduhttp://math.uchicago.edu/~cindy/
Organizer
Daniel Minahan

When do commuting homeomorphisms of S^2 have a common fixed point? Christian Bonatti gave the first sufficient condition: Commuting diffeomorphisms sufficiently close to the identity in Diff^+(S^2) always admit a common fixed point. In this talk we present a result of Michael Handel that extends Bonatti's condition to a much larger class of commuting homeomorphisms. If time permits, we survey results for higher genus surfaces due to Michael Handel and Morris Hirsch, and connections to certain compact foliated 4-manifolds.