Handle friendship seminar 2018 since 2013

Place:University of Tokyo (Komaba campus)
japanese version

2018 Autumn

• The eleventh break 3/15 (Fri) (118)
  Mark Hughes 10:00-12:30
  [Title] Banded unlinks and unit surfaces in CP²
  [Abstract] A unit surface in CP² is an embedded surface which intersects the standard CP¹ in a single transverse intersection point. By work of Melvin, these are related to the Gluck twist surgery operation on CP². With this as motivation, we study unit surfaces via banded unlinks, showing that several classes of these knots are in fact isotopic to the standard CP¹. We also propose an alternate way of viewing these surfaces as closed braids with fold singularities, and several approaches for proving that unit surfaces are standard. This is joint work with Seungwon Kim and Maggie Miller.
  
  
• The tenth break 12/11 (Tue) (123)
  Taketo Sano 10:00-12:30
  [Title] Rasmussen-type invariants from the divisibility of the canonical classes
  [Abstract] We define a family of integer-valued link invariants \hat{s}_c(L; R) each determined by a non-zero non-invertible element c in a domain R. Each \hat{s}_c(L; R) is given by a combination of some classical properties of a diagram D of L, and the �gc-divisibility�h of the canonical class of D in a Khovanov-type link homology determined by (R, c). Similar to Rasmussen�fs s-invariant, each \hat{s}_c is a link-concordance invariant, provides a lower bound for the slice-genus of knot, and gives an alternative proof for the Milnor conjecture. Under some condition, they also define homomorphisms from the knot concordance group to Z. For the special case (R, c) = (Q[h], h), the knot invariant \hat{s}_c coincides with the Rasmussen�fs s-invariant. At the moment we do not know whether there exists a pair (R, c) that gives an invariant distinct from s.
  
  
• The nineth break 11/29 (Thu) ()
  Hiroto Matsuda 10:00-12:30
  [Title] Equivariant corks and groups realizing equivariant corks II
  
  
• The eighth break 11/6 (Tue) (126)
  Hiroto Matsuda 10:00-12:30
  [Title] Equivariant corks and groups realizing equivariant corks
  [Abstract] In this talk , we consider a group G which a weak equivariant cork exists. It is known that there exists the constructions of an H-cork by Auckly-Kim-Melvin-Ruberman, which H is a finite subgroup of SO(4), Z-cork by Gompf and Z^m-cork by Tange. For weak equivariant corks, in addition, there is a weak equivariant cork of any finite Abelian group. In this talk, I will give a brief review of these and after introduce the following result:
  (1) Constructions of equivariant cork for wreath product Z^m and any finite subgroup of SO(4).
  (2) Let G be the group obtained by iterating wreath product for finite cyclic groups. Constructions of equivariant cork for the wreath product of Z^m and G. In particular, (1) is an affirmative answer of a question by Motoo Tange as follows:
  " Are there G-corks for infinite non-commutative group G?"
  The construction is due to a certain combination of previous cork result.
  
  
• The seventh break 10/18 (Thu) (156)
  Masaki Taniguchi 10:00-12:30
  [Title] Rational homology spheres and simply-connected boundings
  [Abstract]
  
  
• The sixth break 10/9 (Tue) (126)
  Motoo Tange 10:00-12:30
  [Title] Ribbon disks immersed handle diagram and handle move
  [Abstract]
  
  

2018 Spring

• The fifth break 7/24 (Tue) (470)
  Moussard Delfine 13:00-15:00
  [Title] A Fox-Milnor theorem for knotted spheres in S⁴
  [Abstract] For knots in the 3-sphere, it is well-known that the Alexander polynomial of a ribbon knot factorizes as f(t)f(1/t) for some polynomial f(t). For 2-knots, i.e. embeddings of a 2-sphere in the 4-sphere, the Alexander polynomial of a ribbon 2-knot is not even symmetric in general. Via an alternative notion of ribbon 2-knots, we give a topological condition on a 2-knot for recovering the factorization of the Alexander polynomial. This is a joint work with Emmanuel Wagner.
  
  
• The fourh break 6/26 (Tue) (426)
  Yuichi Yamada 10:00-12:30
  [Title] Trisection on 4-manifolds with connected boundary
  
  
• The third break 5/15 (Tue) (426)
  Kenta Hayano 10:00-12:30
  [Title] Stability of non-proper stable maps
  
  
• The second break 5/8 (Tue) (426)
  Ayaka Ise 10:00-12:30
  [Title] Diffeomorphism types of homotopy 4-spheres obtained by Gluck surgeries along twist spun 2-knots
  
  
• The first break 4/26 (Tue) (370)
  Hajime Fujita 10:00-12:30
  [Title] Topics on discretization of 1-dimensional manifolds