Handle friendship seminar 2016 since 2013

(In principle, this is an informal seminar related to 4-dimensional manifolds, in practical, every topics are welcome (i.e. physics, chemistry and medicine etc.)
Place:Tokyo Tech (Tokyo Institute of Technology, Ookayama campus)
japanese version

2016 Autumn

• The tenth break 1/24(Tue.) (H230)
  Kouki Sato 10:00-12:30
  [Title] CP²-sliceness and Floer homologycally thin knots
  [Abstrat]If a knot in S³ has thin knot Floer homology, we say that the knot is thin. In this work, we consider which thin knots can bound a disk in CP² - B⁴, and give some obstructions to bounding such a disk. By using the obstructions, we determine which (2,q)-torus knots bound a disk in CP² - B⁴. In addition, we also consider which full-twists can preserve the thinness.<
  
  
• The ninth break 12/13(Tue.) (H230)
  Kenta Hayano 10:00-12:00
  [Title] On the presentation of high dimensional symplectic closed manifold via mapping class group(for study)
  [Abstrat]
  [Reference]
  D. Auroux, Symplectic maps to projective spaces and symplectic invariants, Proceedings of 7th Gokova Geometry-Topology Conference, 1--42.
  
  
• The eighth break 11/1(Tue.) (H230)
  Yuichi Yamada 10:00-12:00  Handout
  [Title] Heegaard Floer theory on lens spaces (For study)
  [Abstrat] First, we review basics on Heegaard Floer theory: They are based on "classic" theory of 3- and 4-dim. manifolds. Especially we focus on 4-manifolds bounded by rational homology spheres. For a lens space, we use the 4-manifold obtained by Hirzebruch-Jung continued fraction. I also talk on d-invariants, and mapping cone theorem on Dehn surgery.
  [Reference]
  • Julian Gibbons, ”Deficiency Symmetries of Surgeries in S³”, International Mathemati cs Research Notices, Vol.2015, No.22, pp.12126?12151.
  • P. Ozsvath and Z. Szabo, "Knot Floer homology and integer surgeries", Algebr. Geom. Topol. 8 (2008), no.1, 101--153.



• The seventh break 10/11(Tue.)(H230)
  Takahiro Oba 10:00-12:30
  [Title] Planar Lefschetz fibrations and Stein structures with distinct Ozsváth-Szabó invariants on corks
  [Abstrat] Thanks to a result of Lisca-Matic and a refinement by Plamanevskaya, it is known that on a 4-manifold with boundary, Stein structures with non-isomorphic spin^c structures induce contact structures with distinct Ozsváth-Szabó invariants. In this seminar, by using corks and Lefschetz fibrations, I show that its converse does not holds, i.e. there are contact structures on the boundary of a 4-manifold such that they have distinct Ozsváth-Szabó invariants and they are induced from the same spin^c structures on the 4-manifold. This talk is based on a joint work with Çağri Karakurt (Boğaziçi Univ.) and Takuya Ukida (Tokyo Tech.).
  [Reference]:
  Cagri Karakurt, Takahiro Oba, Takuya Ukida "Planar Lefschetz fibrations and Stein structures with distinct Ozsváth-Szabó invariants on corks"
  arXiv:1607.07661
  
  
  

2016 Spring

• The sixth break 9/7(Wed.)(H318)
  Hironobu Naoe 10:00-12:30
  [Title] On the acyclic 4-manifolds with shadow complexity 0
  [Abstrat] Any compact oriented smooth 4-manifold is combinatorially presented by 2-dimensional polyhedron which is called shadow. The minimal number of vertices of the shadow is called shadow complexity of the 4-manifold. The classification of closed 4-manifolds with shadow complexity 0 is well-known by Costantino and Martelli. In this talk we consider the version of 4-manifold with boundary. Here we prove that any acyclic 4-manifold with shadow complexity 0 is diffeomorphic to the 4-ball.
  
  
• The fifth break 7/28(Thu.)(H318)
  Kouki Sato 10:00-12:30
  [Title] d-invariant of the double branched covers of Abe-Tagami's knot pair
  [Abstrat] Abe and Tagami give a pair of knots so that the 4-manifolds derived from the 0-framing of the knots are diffeomorphic and the connected sum of one of them and the mirror of the other is not a ribbon knot. It is an open question whether these knots are concordant. In this talk, we show that all d-invariants of the double branched covers of the pair coincide with each other. This is joint work with Jeffrey Meier (Indiana University) and Motoo Tange (University of Tsukuba).
  
  
• The fourth break 6/30(Thu.)(TBA)
  Motoo Tange 10:00-12:30
  [Title] Integration of Υ_K(t)
  [Abstrat] TBA
  
  
• The third break 5/26(Thu.)(TBA)
  Genki Omori10:00-12:30
  [Title] Normal generating system of handlebody subgroup of Torelli group
  [Abstrat] In this talk, I review the generating set of the intersection of the mapping class group of handlebody and the Torelli group of oriented surface. One of our results would be an answer of Problem 2.8 in Chapter 10 in "Problems on Mapping Class Group and Related Topics" by Farb. Also, by this result, I view the generating set of the mapping class group of the intersection of level d mapping class group of oriented surface and the handlebody group.
• The second break 4/28(Thu.)(H318)
  Hokuto Konno 10:00-12:30
  [Title] An invariant of 4-manifolds and adjunction inequalities
  [Abstract] Considering the configuration of surfaces which fail to the adjunction inequality holistically, using Seiberg-Witten theory, we introduce a new 4-dimensional invariant. This is formulated a map from an Abelian group to integers Z. This group is induced by a 4-dimensional manifold and spin^c structures. The nontrivial example of this invariant is obtained from a generalization of a proposition by Ruberman. As an application, we give an adjunction inequality under some condition.
  [References]：
  main reference:
  D. Ruberman “Positive scalar curvature, diffeomorphisms and the Seiberg-Witten invariants”
  http://arxiv.org/abs/math/0105027
  cf.
  D. Ruberman “A polynomial invariant of diffeomorphisms of 4-manifolds”
  http://arxiv.org/abs/math/9911260
  D. Ruberman “An obstruction to smooth isotopy in dimension 4”
  http://arxiv.org/abs/math/9807041
  
  
• The first break 4/21(Thu.)(TBA)
  Kouki Sato  10:00-12:30
  [Title]V_k invariant of cable knots and anti-bipolar topologically slice knots
  [Abstract] V_k invariant for knots is a knot concordance invariant defined from the knot filtration of Heegaard Floer homology for any non-negative intger k . Ni and Wu show that the correction terms of a Dehn surgery along a knot K are computed by the set of V_k invariants. Last year, Wu proved that V_k invariants of the (p,q)-cable of a knot K are computed by the set of V_k of K for any relatively prime positive integers p, q and for any non-negative integer k with k ≤ pq/2. At this time, by using Wu's cable formula, we prove there exist infinitely many topologically slice knots such that they are not smoothly (null-homologous) slice in any simply-connected definite 4-manifold. These examples are so interesting objects in terms of Cochran-Harvey-Horn's bipolar filtration. In this talk, I explain Wu's cable formula and this result.