Boston Graduate Topology Seminar

MIT Meeting

Sunday, April 23, 9:30AM-12:15PM

Math Department, 4th Floor Lecture Room (Building 2, Room 449)

Speakers:

9:30-10:15: Qianhe Qin (Stanford)

Title: An RBG construction of integral surgery homeomorphisms

Abstract: Manolescu and Piccirillo introduced RBG links, a kind of 3-component framed links in S^3, that produce knot pairs with the same 0-surgery. In this talk, I will define n-RBG links, which generalizes their RBG construction to n-surgeries. I will explore potential use of the s-invariant to detect exotic pairs of definite 4-manifolds from a specific type of n-RBG links.

10:30-11:15: Jacob Caudell (BC)

Title: Dehn surgery on knots in the Poincaré homology sphere

Abstract: The Berge Conjecture posits that every integer Dehn surgery on a knot in the three-sphere yielding a three-dimensional lens space arises from Berge's doubly primitive construction. In The lens space realization problem, Greene proves that any lens space that is realized by integer surgery on a knot in the three-sphere is realized by surgery on a knot enumerated in Berge's tabulation of doubly primitive knots in the three-sphere. In this talk, we will demonstrate how to adapt both Berge's doubly primitive construction, which is combinatorial in nature, and Greene's theory of changemaker lattice embeddings---a refinement of embeddings of intersection forms of four-manifolds by data from Heegaard Floer homology---in order to study which lens spaces are realized by surgery on a knot in the Poincaré homology sphere, and report progress on the lens space realization problem for the Poincaré homology sphere.

11:30-12:15: Hokuto Konno (Tokyo)

Title: An exotic diffeomorphism of a contractible 4-manifold

Abstract: We present the first example of an exotic diffeomorphism of a contractible 4-manifold, in a relative sense: the diffeomorphism is topologically isotopic to the identity, fixing the boundary pointwise throughout the isotopy parameter, but there is no such smooth isotopy. Our example is given by a simple way, the Dehn twist along a certain Brieskorn 3-manifold. The proof uses family Seiberg-Witten theory. This is joint work with Abhishek Mallick and Masaki Taniguchi.

Location:

The Mathematics Department is located in Building 2. See Directions and Campus Map.