Handle friendship seminar 2015 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

2015 Autumn

• The 13th break. 3/24(Thu.)(H318)
  Takahiro Oba  10:00-12:00
  [Title]: Open books adapted to canonical contact unit cotangent bundles
  [Abstract] The unit cotangent bundle of a given manifold admits the canonical contact contact structure.
  In this talk, considering the unit cotangent bundle of a Riemann surface,
  I am going to give an explicit description of an open book adapted to this space equipped with the canonical contact structure.
  This is a joint work with Burak Ozbagci (Koç University).
  [Reference]
  T. Oba and B. Ozbagci, Canonical contact unit cotangent bundle. arXiv:1601.05574
• The 12th break.2/18(Thu.)(H318)
  Takayuki Okuda  10:00-12:00
  [Title]: Dehn twist presentation of periodic mapping classes via splitting of singular fibers
  [Abstract] In the last talk, we studied splittability of the stellar singular fiber of a degeneration of Riemann surfaces, in order to decompose its periodic monodromy into right handed Dehn twists. In this talk, supposing that a given singular fiber splits into Lefschetz fibers under barking deformation, we show how to determine the vanishing cycles (describe them explicitly on a general fiber). Using our method, we will obtain new Dehn twist presentations of some periodic mapping classes.
  
  
• The 11th break.11/19(Thu.)(H318)
  Takayuki Okuda  10:00-12:00
  [Title]: Decomposition of periodic mapping classes via splitting of singular fibers
  [Abstract] A splitting of a singular fiber appearing in complex surfaces corresponds to a decomposition of an element of the surface mapping class group, via the topological monodromy around each singular fibers. In particular, given a splitting of a stellar singular fiber into Lefschetz singular fibers, we obtain a product presentation of the corresponding periodic mapping class by right handed Dehn twists. In this talk, we would like to show several results of splittability of singular fibers in terms of such product presentations by illustrating barking deformations.
  
  
• The 10th break.11/1(Thu.)(H318)
  Motoo Tange  10:00-12:00
  [Title]: On finite order cork and its application
  [Abstract] By taking a branched cover along a slice disk of usual cork (akbulut cork) we can construct a finite order cork. We consider application for the corks. Also, in the order 2 case where it contains a canceling pair, we obtain a contractible 4-manifold whose framed link is two slice knots. Then exchanging a slice 1-handle and a 2-handle naturally is a cork twist.
  
  
• The 9th break.10/1(Thu.)(H318)
  Noriyuki Hamada  10:00-12:00
  [Title]: On a double cover of Matsumoto's genus 2 Lefschetz fibration
  [Abstract] Although the obvious fact that taking a finite-degree cover of a Lefschetz fibration/pencil gives another Lefschetz fibration/pencil is a simple idea, it seems to have been rarely considered. In the talk, I will describe a relationship between finite-degree covers of a Lefschetz fibration/pencil and its monodromies, then give as an example covers of Matsumoto's fibration, which I have repeatedly discussed in this seminar. On the other hand, there is a well-known generalization of Matsumoto's fibration to higher genera. I will show that the genus 3 fibration among them is in fact a double cover of Matsumoto's fibration.
  
  Kouki Sato  14:00-15:00
  [Title] On rational bound of prime-power-fold branched cover of slice knot
  [Abstract] Milnor's result concerning infinite cyclic branched cover immediately follows that a prime-power-fold cyclic branched cover of a knot is a rational homology sphere, a prime-power cyclic branched cover of a slice disk is a rational homology 4-ball. In this task we share the proofs of these conclusions. Applying the similar argument, we show that any odd prime-power cyclic branched cover of the (2,1)-cable knot of the figure-8 knot bounds a rational homology 4-ball.
  

• The 8th break. 9/2(Wed.)(H318)
  Tomohiro Asano  10:00-12:00
  [Title] On the symplectic Khovanov homology
  [Abstract] Symplectic Khovanov homology is a link invariant which is defined by Seidel and Smith, and conjectured that it is isomorphic to the original Khovanov homology. For the definition, they use the Lagrangian intersection Floer theory, while Manolescu relates to genus 0 Lefschetz fibration on the disk for the manifold. In this talk, focusing on the construction of the spaces, we review the definition of symplectic Khovanov homology.
  [References]
  P. Seidel and I. Smith. A link invariant from the symplectic geometry of nilpotent slices. Duke Math. J. 134:453-514, 2006.
  C. Manolescu. Nilpotent slices, Hilbert schemes, and the Jones polynomial. Duke Math. J., 132:311-369, 2006.
  
  
  
• The 7th break. 9/1(Tue.)(H318)
  Hokuto Konno  10:00-12:00
  [Title]: Configuration of embedded surfaces in 4-manifolds and genus bound.
  [Abstract] We explain that in the case where self-intersection 0 surfaces are embedded in a 4-manifold at least one surface in their surfaces has a genus bound. This result is shown by considering a family of a Seiberg-Witten equation with embedded surfaces data. As an application we obtain restrictions to the genus of a pair of two surfaces and alternative proof of Strle's adjunction inequality.
  [Reference]
  Hokuto Konno, gBounds on genus and configurations of embedded surfaces in 4-manifoldsh
  http://arxiv.org/abs/1507.00139
  
  
• The 6th break. 7/28(Tue.)(H318)
  Yuichi Yamada  10:00-12:00
  [Title] Dehn surgery on Minimally twisted five chain link
  [Abstract] Research area ``Lens space surgery" is facing a turning point: Ex. counter examples of lens space surgeries from the Poincare sphere that do not belong to Tange-Rasmussen's list ([Baker]). One reason seems that ``lens space surgery from lens space" comes in our target. I will talk about Dehn surgery on the Minimally twisted five chain link (results in [MPR] and [BDH]), which is a start point of recent development. For handle friendship, I will demonstrate some handle calculus.
  [References]
  [MPR] B.Martelli, C.Petronio and F.Roukema,
  Exceptional Dehn surgery on the minimally twisted five-chain, Comm. Anal. Geom. 22 (2014) no.4, 689-735.
  [BDH] K.Baker, B.G.Doreshal and N.Hoffman,
  On manifolds with multiple lens space fillings, Bol.Soc.Mat.Mex. 20 (2014), 405-447.
  
  
• The 5th break. 7/14(Tue.)(H318)
  Kouki Sato  10:00-12:00
  [Title] On the obstruction of topological sliceness of knots
  [Abstract] Guided by Collins' thesis, I review typical invariants describing the obstruction of topological sliceness of a knot: L²-signature, Casson-Gordon invariants, and twisted Alexander polynomial.
  Reference:
  Collins, On the concordance orders of knots. arXiv:1206.0669(2012).
  
  
• The 4th break. 6/23(Tue.)(H318)
  Abe Tetsuya  10:00-12:00
  [Title] The Dehornoy ordering of braids
  [Abstract] We give a brief review of a left-ordering of braids, called the Dehornoy ordering. We also explain the orderability of the fundamental group of a 3-manifold.
  
  
• The 3rd break. 6/16(Tue.)(H318)
  Erika Kuno  10:00-12:00
  [Title] Geometric group theory and uniform hyperbolicity for curve graphs
  [Abstract] Geometric group theory is a new field investigating the structures of groups from a geometric viewpoint. In this field, ``Gromov hyperbolicity" is one of the most important ideas. In this talk, we will first describe basic and important ideas in Geometric group theory, in particular Gromov hyperbolicity. After that, we will state our main results, that is, the uniform hyperbolicity for arc graphs, curve graphs, and arc-curve graphs of non-orientable surfaces. Finally, we will give an outline of a proof of the uniform hyperbolicity for curve graphs of non-orientable surfaces.
  
  
• The 2nd break. 5/19(Tue.)(H318)
  Motoo Tange  10:00-11:00
  [Title] The slice-ness of twisted Whitehead double of 3₁ and Heegaard Floer homology
  [Abstract] We investigate slice-ness of twisted Whitehead double D₊(3₁,n). If time permitted, we determine HF⁺ of integer (or half-integer) surgery of 3₁#3₁ with introduction of the way to compute Heegaard Floer homology.
  [Reference]
  Motoo Tange, Heegaard Floer homology of Matsumoto's manifolds
  
  Kouki Sato  11:00-12:00
  [Title] Heegaard Floer correction terms of (+1)-surgeries on (2,q)-cablings
  [Abstract]:
  
  
• The 1st break. 4/14(Tue.)(H318)
  Norihuki Hamada  10:00-12:30
  [Title] Sections of Matsumoto's genus 2 Lefschetz fibration II
  [Abstract] I constructed two new 4-tuples of disjoint (-1)-sections of the Matsumoto fibration, which we previously discussed. Altogether with those I introduced last time, we have four such 4-tuples. We observe an interesting phenomenon compared to the homology of the total space of the fibration. I would like to discuss about those things.