Handle friendship seminar since 2013

• The 1st break. 4/24(Wed.)(Honkan335)
  Motoo Tange  10:00-12:00Note
  [Title]: Brieskorn manifolds in E(1)
  [Abstract]: We give some embeddings of Σ(2,3,6(2n-1)−1) (1≤ n≤15) in E(1). Each of the decompositions induced by the embeddings in E(1) gives rise to Gompf's nuclei and a −E₈ manifold (it is a 4-manifold with HZS³ boundary whose intersection form is −E₈). Furthermore, the construction can give (−29)-sphere representing some class in H₂(E(1)).
  
  
• The 2nd break. 5/1(Wed.)(Honkan206)
  Motoo Tange  10:00-12:00, 13:00-15:00Note
  [Title]: Log transform, knot surgery, Fintushel-Stern and Park's exotic rational surfaces.
  [Abstract]: The definition of log transform and how to describe. The picture of Fintushel-Stern's knot surgery. The monodromy of ellipitic fibration. The rational blow-down. The relationship between log transformation and rational blow down. Park's exotic CP²#^8,7-CP², and Fintushel-Stern's exotic CP²#⁶-CP²
  
  
• The 3rd break. 5/15(Wed.)(Honkan335)
  Motoo Tange  10:00-12:00Note
  [Title]: Akhmedov-Park's exotic manifolds, 4-dimensional torus, Cappell-Shaneson spheres．
  [Abstract]: Akhmedov-Park's exotic CP²#³-CP² construction．Luttinger surgery． symplectic manifolds surgery． How to describe 4-dimensional torus.How to describe T²×Σ_g. Akbulut's hooking and roping．How to describe the Cappell-Shaneson spheres．
  
  
• The 4th break. 6/12(Wed.)(Honkan 206)
  Yuichi Yamada  10:00-12:00    Note
  [Title]：Torus knots and lens spaces
  [Abstract]：Torus knot has a fundamental geometric structure, and it is interesting objects widely-related to algebraic curves and singularity theory as well as low-dimensional topology. We explain why a Dehn surgery along any torus knot gives rise to a lens space, by a handle-seminar-like method. (This abstract is translated by Tange.)
  
  
• The 5th break. 6/19(Wed.)(Honkan 206)
  Tetsuya Abe  10:00-12:00   Note
  [Title]: Property nR conjecture and slice-ribbon conjecture
  [Abstract]:I introduce the well-known facts about Generalized Property nR conjecture and Property nR In particular, I show that Cappell-Chaneson (homotopy) 4-spheres）give potential counterexamples of Property 2R conjecture and slice-ribbon conjecture, Also, I exaplain that such examples has higher potential counterexamples.(Translated by Motoo Tange)
  [Reference] R.Gompf, M.Scharlemann and A.Thompson, Fibered knots and potential counterexamples to the Property 2R and Slice-Ribbon Conjectures, Geometry & Topology 14 (2010) 2305–2347
  
  
• The 6th break. 6/26(Wed.)(Honkan 206)   Note Horikawa surfaces
  Motoo Tange  10:00-12:00
  [Title]: Branched cover and its application
  [Abstract]; Some topics related to branched cover of 4-manifolds.
  [Reference] R.Gompf, A.Stipsicz, 4-manifolds and Kirby calculus, Graduate Studies in Mathematics, 20. American Mathematical Society, Providence, RI, 1999



• The 7th break. 7/4(Thr.)(Honkan 225)
  Yuichi Yamada  10:00-12:00 Note    Grape-Note    Resume
  [Title]: Divide knots and Kirby-Melvin' grapes
  [Abstract]: The "grapes" defined by Kirby--Melvin is a connected union of some circles in the circle pakcking of the plane. Each grapes defines a 4-manifold of special type, especially a piece of complex surfaces, via Kirby diagram. It is related to "divide knots" in my last talk. I would like to show you how convenient the method is.
  [Reference] R. Kirby and P. Melvin, The E₈-manifold, singular fibers and handlebody decompositions. Proceedings of the Kirbyfest (Berkeley, CA, 1998), 233–258, Geom. Topol. Monogr., 2, Geom. Topol. Publ., Coventry, 1999.
  
  
• The 8th break. 7/16(Tue.)(Honkan H220→H206)
  Motoo Tange  10:00-11:00
  [Title]: Cork, plug and local moves of 4-manifolds
  [Abstract]: I will review cork and plug. Specially I explain how Akbulut-Yasui's cork and plug give exotic 4-manifolds. I will define a plug with infinite order for between knot surgeries and generalize it. If time allows, we argue some plugs for local moves for knots or plugs with finite order.
  [Reference] S. Akbulut, and K. Yasui, Corks, Plugs and exotic structures, Jour. of GGT, vol 2 (2008) 40-82.
  M. Tange, A plug with infinite order and some exotic structures,（Under construction.）
  
  Masatsuna Tsuchiya  11:00-12:00   Note
  [Title]: On the existence of Corks
  [Abstract]: We will introduce the paper on the existence of corks by R. Matveyev.
  [Reference] R. Matveyev, A decomposition of smooth simply-connected h-cobordant 4-manifolds, J. Differential Geom. 44 (1996), no. 3, 571–582
  
  
• The 9th break. 7/25(Sat.)(Honkan H206)
  Masatsuna Tsuchiya  10:00-   Note
  [Title]: On the existence of Corks
  [Abstract]: We will introduce the paper on the existence of corks by R. Matveyev.
  [Reference] R. Matveyev, A decomposition of smooth simply-connected h-cobordant 4-manifolds, J. Differential Geom. 44 (1996), no. 3, 571–582
  
  

• The 10th break. 10/18(Fri.)(Honkan H318)
  Masatsuna Tsuchiya  13:00-
  [Title]: On the homology 3-spheres presented by two trefoil knots.
  [Abstract]: Consider the homology spheres presented by two trefoil knots whose linking number is 1 and framings are 0, n respectively. We denote the homology spheres by W_n. We show that when n is an odd integer, W_n does not bound any contractible 4-manifold.
  There are some well-known facts on this topics as follows.
  - In the case of n=0, Akbulut [A] proved that W_n does not bound any contractible 4-manifold.
  - In the case of n=6, Maruyama [M] proved that W_n bounds a contractible 4-manifold.
  [Reference]
  [A] S. Akbulut, A Note on a Homology Sphere, PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY Vol.125, Number 2, February 1997, 625-628
  [K] Rob Kirby (compiler), Problems in Low Dimensional Manifold Theory, Proceedings of Symposia in Pure Mathematics, Vol.32, (1978), 273-312. MR 80g:57002
  [M] N Maruyama, Knot Surgery Description of Some Closed Orientable 3-Manifolds, JOURNAL OF TSUDA COLLEGE, Vol.16,(1984),1-14.
  [T] M.Tsuchiya, On homology 3-spheres defined by two knots, arXiv:1401.7445
  
  
  
  Here we put the note about the Heegaard Floer homology of Matsumoto's manifolds.(Here.)
  
  
• The 11th break. 11/1(Fri.)(H318)
  Takahiro Oba  13:00-14:30
  [Title]: Mazur manifolds admitting genus 0 PALF.
  [Abstract]: I show that some Mazur manifolds, which are orientable, compact, contractible 4-manifolds but not S³, admit PALF structures whose general fibers are 3-holes disks. From contact topological point of view, I refer to the reason why we consider such manifolds.
  
  Tetsuya Abe  15:00-16:00
  [Title]: Infinitely many ribbon disks with the same exterior.
  [Abstract]: When I talked at the Friday seminar in Osaka city University, I constructed an infinite family of ribbon disks from the annulus twist of 8₂₀. In this talk, we show that we can easily get infinite families of ribbon disks by iterating annulus twist of ribbon presentations of other knots.
  
  
• The 12th break 11/22（Fri.）(H318)
  Motoo Tange  13:00-14:30
  [Title]: 2-equivlalence class and ribbon surface tangle
  [Abstract]: Any 4-dimensional 2-handlebody is a branched over over ribbon surface in 4-ball. In the paper below, they gave the complete relations between two ribbon surface tangles which give the same 2-equivalence class. In this talk, we aim the construction of an invariant for 4-dimensional 2-handlebody up to 2-equivalence class.
  [Reference]
  I.Bobtcheva and R.Piergallini On 4-dimensional 2-handlebodies and 3-manifolds. J. Knot Theory Ramifications 21 (2012), no. 12, 1250110, 230 pp.
  
  
• The 13th break 1/17（Fri.）(Honkan H235)
  Motoo Tange  13:00-Note
  [Title]: Some plug twists with infinite order and Seiberg-Witten invariant
  [Abstract]:We introduce the plug with infinite order. We detect some infinite exotic structures obtained from the plug twist by using Seiberg-Witten invariant. Also, we give some obstruction for the cork with infinite order by using Heegaard Floer 4-manifold invariant.
  
  
• The 14th break 2/14（Fri.）(Honkan H318)
  Takuya Ukita  13:00-14:30
  [Title]: A PALF structure of Akbulut-Yasui cork and cork twist
  [Abstract]:I will talk about a construction of a genus 0 PALF for the Akbulut-Yasui cork which is a kind of Stein surfaces.
  
  Takahiro Oba  15:00-
  [Title]: On Mazur manifolds admitting genus 0 PALF
  [Abstract]: I will report the existence of infinitely many Mazur type homology spheres admitting genus 0 PALF with 4-holed-sphere-fiber. This result is a generalization of my previous talk in the handle seminar.
  
  
• The 15th break 3/4（Tue.）(Honkan H318)
  Kouki Sato  13:00-
  [Title]: CP²-genus of knots and its application
  [Abstract]:I will introduce the application of the CP²-genus of knots to detection of CP²'s exotic structures.
  
  Yuichi Yamada  (soon after Sato's talk.)
  [Title]: The knot 8₂₀
  [Abstract]:8₂₀ is a ribbon, fibered knot treated in Abe-Jong-Omae-Takeuchi's paper and, as a remarkable property, its 0-surgery is obtained by 0-surgery of another knot . This talk will be organized as follows:
  (1) Investigate the monodromy.
  (2) Check that the 0-surgery is a graph manifold.
  (3) Clarify the relationship with the Mazur (and false Mazur) manifold.
  (4) Observe an unexpected emergence of exceptional surgery in this context.
  I seem that such consideration connects to each study of the members of handle seminar, and so if this talk can help them, it will be a pleasure for me.
  [Reference]
  Abe, Jong, Omae and Takeuchi, Annulus twist and diffeomorphic 4-manifolds, Mathematical Proceedings of the Cambridge Philosophical Society 155 (2013), 219-235.
  
  
• The 16th break 3/26（Wed.）(H318)
  Tetsuya Abe  13:00-
  [Title]: A consequence of the talk "The knot 8₂₀"
  [Abstract]:Abe. Jong, Omae and Takeuchi constructed mutually different infinite sequence {K_i} from the knot 8₂₀
  
  X(8₂₀, 0) ~~ X(K₁, 0)~~X(K₂, 0)~~・・・ Here ~~ menas a diffeomorphism. X(K,m) stands for a 4-ball attaching 2-handle along K with framing m. In this talk, we show that for any n there exists an infinite sequence {J_i} such that X(8₂₀, n) ~~ X(J₁, n)~~X(J₂, n)~~・・・ In the rest of my talk, I show that the knots J_i are mutually different.
  This work is a joint work with Jong.
  [Reference]
  Abe. Jong, Omae and Takeuchi, Annulus twist and diffeomorphic 4-manifolds, Mathematical Proceedings of the Cambridge Philosophical Society 155 (2013), 219-235.