SU(2) representations of small Dehn surgeries on knots

Speaker:

Fan Ye

Affiliation:

Harvard University

Date:

Thu, 15/06/2023 - 12:00 - 13:00

Location:

MPIM Lecture Hall [2]

Parent event:

Low-dimensional topology seminar [3]

Contact: Aru Ray (aruray @ mpim-bonn.mpg.de)

Kronheimer-Mrowka proved that the fundamental group of r-surgery on a nontrivial knot for |r|<=2 always has an irreducible SU(2) representation, which answered the property P conjecture affirmly. They asked the case of r=3 and 4. The case r=4 was solved by Baldwin-Sivek and the case r=3 was solved by Baldwin-Li-Sivek-Ye. In this talk, I will describe the strategy of the proofs using instanton Floer homology.