Handle friendship seminar 2017 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

2017 Autumn

• The fourth break 10/16 (Mon.) (H213)
  Motoo Tange 9:45-11:45
  [Title] Bordered Floer homology and torus-sum formula 2
  [Abstrat] We talk about a sequel of previous break.
  
  
• The fourth break 10/16 (Mon.) (H213)
  Motoo Tange 9:45-11:45
  [Title] Bordered Floer homology and torus-sum formula
  [Abstrat] R. Lipshitz, P. Ozsvath and D. Thurson defined bordered Heegaard Floer homology for a bordered 3-manifold. In this talk, I will give a brief review. As an example, for two 3-manifolds with torus boundary we study Heegaard Floer homology of the 3-manifold obtained by gluing the two manifolds along the tori.
  [References]
  M. Hedden, A. S. Levine, Splicing knot complements and bordered Floer homology, J. Reine Angew. Math. (2016) 129--154
  J. Hanselman, Splicing integer framed knot complements and bordered Heegaard Floer homology, arXiv:1409.1912 to appear Quantum Top.
  
  

2017 Spring

• The third break 9/26 (Tue.) (H318)
  Takahiro Oba 10:00-12:30
  [Title] Surfaces in D⁴ with the same boundary and fundamental group
  [Abstrat] Some transverse links in the standard contact 3-sphere can be realized as boundaries of symplectic surfaces in the standard symplectic 4-disk. There are a few examples of transverse knots or links which bound district symplectic surfaces, which can be distinguished by the fundamental groups of their complements. In this talk, I give a family of transverse knots bounding two distinct symplectic surfaces whose complements have isomorphic fundamental groups.
  
  
• The second break 5/18 (Thu.) (H318)
  Masaki Taniguchi 10:00-12:30
  [Title] The moduli spaces of the ASD equations on 4-manifolds on a periodic end and obstruction to embeddings of 3-manifolds
  [Abstrat] For a pair of an oriented closed 3-manifold and an oriented closed 4-manifold satisfying a certain homological condition we construct in filtered instanton Floer cohomology with degree 1 an obstruction class to exist an embedding related to the pair with some homological condition. This obstruction class is obtained by applying Donaldson's method counting the flows going into the trivial flat connection in a filtered instanton Floer homology (depending on the values of the Chern-Simons functional). The proof for ``this class" to be indeed the obstruction class is obtained by discussing the compactness of the moduli space of the ASD equations on non-compact 4-manifolds with a periodic end. As an application, we prove that there exists no embedding from homology spheres which the Froyshov invariant (defined in instanton Floer theory) is not zero to any homotopy S¹×S³ which generates H₃.
  
  
• The first break 4/20 (Thu.) (H318)
  Kouki Sato 10:00-12:30
  [Title] A partial order on nu+ equivalence classes
  [Abstrat]
  The nu+ equivalence is an equivalence relation on the knot concordance group. Hom proves that many concordance invariants derived from Heegaard Floer homology are invariant under nu+ equivalence. In this work, we introduce a partial order on nu+ equivalence classes, and study its algebraic and geometrical properties. As an application, we prove that any knot with genus 1 is nu+ equivalent to any of the unknot, the trefoil and its mirror.
  [Reference]
  J. Hom, A survey on Heegaard Floer homology and concordance, J. Knot Theory Ramifications 26 (2017), no. 2, 1740015, 24 pp.
  M. H. Kim and K. Park, An infinite-rank summand of knots with trivial Alexander polynomial, arXiv:1604.04037.