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.
Links:
[1] https://www.mpim-bonn.mpg.de/de/taxonomy/term/39
[2] https://www.mpim-bonn.mpg.de/de/node/3444
[3] https://www.mpim-bonn.mpg.de/de/node/12018