Orateur: Nicholas
Zufelt (Imperial College,London)
Titre: The combinatorics
of reducible Dehn surgeries.
Résumé:
The proposed classification of reducible Dehn surgeries on knots in
the three-sphere is known as the Cabling Conjecture. A large amount of
progress toward the conjecture has been established which forces an
arbitrary reducible surgery to coarsely resemble the cabled reducible
surgery. In a similar spirit, it should be the case that all reducible Dehn
surgeries on nontrivial knots give precisely two irreducible connected
summands, sometimes referred to as the Two Summands Conjecture. Using the
main combinatorial object appearing first in the proof of the Knot
Complement Problem due to Gordon and Luecke, we are able to restrict any
surgery coefficient producing more than two summands to being less than or
equal to the bridge number of the purported knot. A consequence of this is
the completion of the Two Summands Conjecture for positive braid closures.