Handle friendship seminar 2019 since 2013

Place:University of Tokyo (Komaba campus)
japanese version

2019 Autumn

• The ninth break 1/16 (Thu.) (TBA)
  Masaki Taniguchi 10:00-12:30
  [Title] Seifert hypersurfaces of 2-knots and Chern-Simons functional
  [Abstract]
  
  
• The eighth break 11/26 (Tue.) (370)
  Mizuki Fukuda 10:00-12:30
  [Title] Gluck twists along 2-knots with periodic monodromy
  [Abstract]
  
  

2019 Spring

• The seventh break 9/25 (Wed.) (156)
  Nobuo Iida 10:00-12:30
  [Title] A Bauer-Furuta type refinement of Kronheimer-Mrowka's invariant for 4-manifolds with contact boundary
  [Abstract]
  
  Yoshinori Asano 14:15-16:45
  [Title] Vertical 3-manifolds in simplified genus 2 trisection of 4-manifolds
  [Abstract]
  
  
• The sixth break 8/26 (Mon.) (306)
  Hiroto Masuda 10:00-12:30
  [Title] On the mapping class groups of exotic R⁴
  [Abstract]
  [Reference] R. Gompf Group actions, corks and exotic smoothings of R⁴, Invent. Math. 214(2018)3, 1131--1168
  
  
• The fifth break 7/30 (Tue.) (426)
  Hironobu Naoe 10:00-12:30
  [Title] Shadows of acyclic 4-manifolds with sphere boundary II
  [Abstract]



• The fourth break 7/9 (Tue.) (156)
  Kouki Sato 10:00-12:30
  [Title] Filtered instanton Floer homology and the homology cobordism group II
  [Abstract]
  
  
• The third break 6/26 (Wed.) (156)
  Hironobu Naoe 10:00-12:30
  [Title] Shadows of acyclic 4-manifolds with sphere boundary
  [Abstract]
  
  
• The second break 6/19 (Wed.) (156)
  Kouki Sato 10:00-12:30
  [Title] Filtered instanton Floer homology and the homology cobordism group
  [Abstract] Fintushel-Stern and Furuta developed orbifold gauge theory to prove that an infinite family of Brieskorn 3-spheres are linearly independent in the homology cobordism group. In this work, by translating their work into the words of filtered instanton Floer homology, we introduce a family {r_s} of real-valued homology cobordism invariants, which is parametrized by non-positive real numbers (with negative infinity). As an application of the invariants, we give infinitely many homology 3-spheres which cannot bound any definite 4-manifold. As another application, we show that if the 1-surgery of a knot has negative Froyshov invariant, then all positive 1/n-surgeries of the knot are linearly independent in the homology cobordism group.
  
  In the first half of this talk, we give a overview of our work. In the second half, we focus on (1) connected sum formula for r₀ (used for proving linear independence), (2) the relationship to Daemi's homology cobordism invariants (used for computation of r_s for some Brieskorn 3-spheres), and (3) topological applications of r_s. This is a joint work with Yuta Nozaki and Masaki Taniguchi.
  
  
• The first break 4/23 (Tue.) (156)
  Marco De Renzi 10:00-12:30
  [Title] Renormalized Hennings invarinats and TQFTs
  [Abstract] Non-semisimple constructions in quantum topology produce strong invariants and TQFTs with unprecedented properties. The first family of non-semisimple quantum invariants of 3-manifolds was defined by Hennings using certain algebraic ingredents called unimodular ribbon Hopf algebras. This enabled Lyubashenko to build mapping class group representations in the special case of factorizable ribbon Hopf algebras. Further attempts at extending these constructions to TQFTs only produced partial results, as the vanishing of Hennings invariants in many crucial situations made it impossible to treat the case of non-connected surfaces. We will show how to overcome these problems. In order to do so, we will first renormalize Hennings invariants through the use of modified traces. In the factorizable case, we will further show that the universal construction of Blanchet, Habegger, Masbaum, and Vogel produces a fully monoidal TQFT yielding mapping class group represen- tations in Lyubashenko’s spaces. We will also briefly discuss recent results relating these constructions to other non-semisimple quantum invariants and TQFTs. This is a joint work with Nathan Geer and Bertrand Patureau.