Handle friendship seminar 2023 since 2013

Place:online or University of Tokyo (Komaba campus) or Online
japanese version

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2023 Autumn

• The fourth break 3/22 (Fri.) (Zoom meeting)
  Jin Miyazawa 10:00-12:30 (GMT +09:00)
  [Title] A gauge theoretic invariant of embedded surfaces in 4-manifolds and exotic $P^2$-knots
  [Abstract]e give an infinite family of embeddings of $RP^2$ to $S^4$ such that they are mutually topologically isotopic however are not smoothly isotopic to each other. Moreover, they are topologically isotopic to the standard $P^2$-knot. To prove that these $P^2$-knots are not smoothly isotopic to each other, we construct a gauge theoretic invariant of embedded surfaces in 4-manifolds using a variant of the Seiberg--Witten theory, which is called the Real Seiberg--Witten theory.


• The third break 3/4 (Mon.) (Zoom meeting)
  Hajime Kubota 10:00-12:30 (GMT +09:00)
  [Title] On grid homology and connected sums of knots
  [Abstract]Grid homology is a purely combinatorial knot invariant which is isomorphic to knot Floer homology. Using grid homology, we can compute knot Floer homology combinatorially without geometric difficulties of it. Therefore it is an interesting problem whether the results of knot Floer homology can be proved in the framework of grid homology. In this talk, we first introduce the definition and computational algorithm of grid homology, then prove a K\"{u}nneth formula of connected sums of knots.


• The second break 2/6 (Tue.) (Zoom meeting)
  Koichi Tauchi 10:00-12:30 (GMT +09:00)
  [Title]
  [Abstract]
  

2023 Spring

• The first break 9/12 (Tue.) (Zoom meeting)
  Jacob Caudell 9:00-11:30 (GMT +09:00)
  [Title] E₈-changemaker lattices and Tange knots
  [Abstract]The Berge Conjecture asserts that Berge's elegant doubly primitive construction accounts for all lens space surgeries on knots in the 3-sphere. Berge's construction easily generalizes to produce knots in any Heegaard genus 2 integer homology sphere, and in 2007 Tange compiled a list of doubly primitive knots in the Poincare homology sphere, P. We build on Greene's work on changemaker lattices, which he used to resolve the lens space realization problem for the 3-sphere, and develop the notion of an E₈-changemaker lattice. We provide an account of knots in P with lens space surgeries, and explain how we use E₈-changemaker lattices to prove the following:
  
  Theorem (C. 2023): Let K be a knot in P, and let p be a positive integer with p > 2g(K)-1. If K(p) is the lens space L(p, q), then there is a Tange knot T in P such that T(p) = L(p, q), and HFK(P, K) = HFK(P, T).