East Asia Knot School 4: Abstract (JAPAN and abroad)

Abstract (Participants of Japan Group)

Plenary Talks China Japan+ Korea Poster TalkSchedule

Title : Network of Seifert surgeries [Poster]
--- joint works with Mario EUDAVE-MUNOZ, Katura MIYAZAKI, Kimihiko MOTEGI
Speaker : Arnaud Deruelle (Tokyo Insitute of Technology)
Abstract :

Title : Boundaries of incompressible surfaces in graph link exteriors [PDF]
Speaker : Toru Ikeda (Kochi University)
Abstract :

Title : Braid ordering, Nielsen-Thurston classification and geometry of knot complement [Poster]
Speaker : Tetsuya Ito (Graduate School of Mathematical Sciences, The University of Tokyo)
Abstract :

Title : A $G$-family of quandles and cocycle invariants for handlebody-links [Poster]
--- (joint work with Atsushi Ishii (RIMS, Kyoto University))
Speaker : Masahide Iwakiri (Osaka City University (OCAMI))
Abstract :

Title : Genus 2 Heegaard splittings of 3-manifolds and 3-bridge presentations of links [Poster]
Speaker : Yeonhee Jang (Osaka University)
Abstract :

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Title : On the Alexander polynomials of alternating knots of genus two [PDF]
Speaker : In Dae Jong (Osaka City University)
Abstract :

Title : Lens surgeries along the Whitehead link
--- (joint work with Noriko Maruyama (Musashino Art University) and Masafumi Shimozawa (Tokyo Woman's Christian University))
Speaker : Teruhisa Kadokami (Department of Applied Mathematics, Dalian University of Technology)
Abstract :

Title : The Homfly polynomial of braids with a full twist [PDF]
Speaker : Tamas Kalman (JSPS, Graduate School of Mathematical Sciences, The University of Tokyo)
Abstract :

Title : On bridge presentation of virtual knots [PDF]
Speaker : Seiichi Kamada (Hiroshima University)
Abstract :

Title : Third rack homology class of knot quandle obtained from shadow coloured diagram [Poster]
Speaker : Yasto Kimura (Graduate School of Mathematical Sciences, The University of Tokyo)
Abstract :

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Title : An asymptotic behavior of the dilatation for a family of pseudo-Anosov braids [PDF]
--- (joint work with Mitsuhiko Takasawa)
Speaker : Eiko Kin (Tokyo Institute of Technology)
Abstract :

Title : Isometries on SU(2)-representation spaces of knot groups and twisted Alexander functions [Poster]
Speaker : Takahiro Kitayama (Graduate School of Mathematical Sciences, The University of Tokyo)
Abstract :

Title : O(2N) and Sp(N)-version of the LMO invariant as a matrix model
Speaker : Takahito Kuriya (Kyushu University, Faculty of MATHEMATICS)
Abstract :

Title : Applications of braid group representations to dynamical systems [PDF]
Speaker : Takashi Matsuoka (Naruto University of Teacher Education)
Abstract :

Title : On the signature cocycle and related invariants of 3-manifolds [PDF]
Speaker : Takayuki Morifuji (Tokyo Univ. Agri. & Tech.)
Abstract :

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Title : Essential surfaces and torus knots with twists [PDF]
Speaker : Kanji Morimoto (Department of IS and Mathematics, Konan University)
Abstract :

Title : Surgery presentations of the dihedral covering link [PDF]
Speaker : Daniel Moskovich (RIMS, Kyoto Univ.)
Abstract :

Title : On logarithmic knot invariant [PDF]
Speaker : Jun Murakami (Waseda University)
Abstract :

Title : Knot related patterns in folk arts [Poster]
Speaker : Shojiro Nagata (InterVision��Institute)
Abstract :

Title : Delta unknotting numbers for positive knots
Speaker : Takuji Nakamura (Osaka Electro Communication university)
Abstract :

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Title : On spatial graph diagrams with at most three crossings [PDF]
--- (joint work with Youngsik Huh (Hanyang University))
Speaker : Ryo Nikkuni (Faculty of Education, Kanazawa University)
Abstract :

Title : Dynamics of gradient flows in the non-transversal Morse theory [PDF]
Speaker : Andrei Pajitnov (Universite de Nantes)
Abstract :

Title : On the Heegaard genus of knot exteriors
--- (joint with Tsuyoshi Kobayashi)
Speaker : Yo'av Rieck (the University of Arkansas)
Abstract :

Title : Configuration space integral and Poisson structure on the homology of the space of framed long knots [Poster]
Speaker : Keiichi Sakai (The University of Tokyo)
Abstract :

Title : On tricolorable 2-knots of triple point number four
Speaker : Shin Satoh (Kobe University, Department of Mathematics��
Abstract :

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Title : On charts with two crossings [PDF]
--- (joint work with Teruo Nagase)
Speaker : Akiko Shima (Department of Mathematics, Tokai University)
Abstract :

Title : Spatial graph diagrams realizing prescribed subdiagrams partitions [PDF]
Speaker : Reiko Shinjo (Osaka City University Advanced Mathmatical Institute)
Abstract :

Title : Determinants of knots and Diophantine equations [PDF]
Speaker : Alexander Stoimenow (Osaka City Univ.)
Abstract :

Title : On the number of $SL(2;{\mathbb Z} / p {\mathbb Z})$-representations of knot groups
Speaker : Teruaki Kitano (Soka University) and Masaaki Suzuki (Akita University)
Abstract :

Title : Entropy of pseudo-Anosov braids and fiber surfaces of hyperbolic 3-manifolds
--- (joint work with Eiko Kin)
Speaker : Mitsuhiko Takasawa (Tokyo Institute of Technology, Dept. of Mathematical and Computing Sciences)
Abstract :

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Title : A categorification of the one-variable Kamada-Miyazawa polynomial [PDF]
--- (joint work with Atsushi ISHII (RIMS, Kyoto University))
Speaker : Kokoro Tanaka (Gakushuin University)
Abstract :

Title : An infinite family of exotic 4-manifolds and Rasmussen invariants of knots [PDF]
Speaker : Toshifumi Tanaka (Osaka City University Advanced Mathematical Institute)
Abstract :

One of the biggest break-throughs in 4-dimensional topology was Freedman's proof 
that every Casson handles is homeomorphic to the standard open 2-handle
since it was used in a proof of Poincar\'e conjecture in dimension 4.
On the other hand, R. Gompf showed that there exist infinitely many 
diffeomorphism types of Casson handles by using gauge theory, and
\v{Z}. Bi\v{z}aca gave an explicit example of a Casson handle which is not 
diffeomorphic to the standard open 2-handle.
Such a Casson handle is called exotic. Many Casson handles are exotic, 
however, it is still not known if all of them are. In this talk, 
by using Rasmussen's invariant derived from Khovanov theory, 
we give a gauge-theory free proof for the existence of 
countably many exotic Casson handles in a family of Casson handles. 
On the other hand, by using Bohr's inequality about the kinkiness of knots, 
derived via gauge theory, we distinguish between any two Casson handles in the family. 
Finally, we discuss some problems about smooth structures of Casson handles 
and other non-compact smooth 4-manifolds.

Title : A design for pseudo-Anosov braids using hypotrochoid curves
Speaker : Saki Umeda (Graduate School of Humanities and Sciences, Nara Women's University)
Abstract :

Title : On the geometry of certain slices of character varieties of knots [PDF]
--- (joint work with Fumikazu Nagasato)
Speaker : Yoshikazu Yamaguchi ( Graduate School of Mathematical Sciences, The University of Tokyo)
Abstract :

Title : On lower bounds of triple point numbers for 5-colorable 2-knots [PDF]
Speaker : Tsukasa Yashiro (Sultan Qaboos University)
Abstract :

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Title : Self delta-equivalence for links whose Milnor's isotopy invariants vanish
Speaker : Akira Yasuhara (Tokyo Gakugei University)
Abstract :

For an $n$-component link $L$, the Milnor's isotopy invariant is defined for each 
multi-index $I=i_1i_2...i_m~(i_j\in\n)$. Here $m$ is called the length. 
Let $r(I)$ denote the maximum number of times that any index appears. 
It is known that Milnor invariants with $r=1$ are link-homotopy invariant. 
N.~Habegger and X.~S.~Lin showed that two string links are a link-homotopc 
if and only if their Milnor invariants with $r=1$ coincide. 
This gives us that a link in $S^3$ is link-homotopic to a trivial link if and only if 
the all Milnor invariants of the link with $r=1$ vanish. 
Although Milnor invariants with $r=2$ are not link-homotopy invariants,   
T.~Fleming and the speaker showed that Milnor invariants with $r\leq 2$ 
are self $\Delta$-equivalence invariants. 
In this talk, we give a self $\Delta$-equivalence classification of 
the set of $n$-component links in $S^3$ whose Milnor invariants with length $\leq 2n-1$ 
and $r\leq 2$ vanish. As a corollary, we have that 
a link is self $\Delta$-equivalent to a trivial link if and only if 
the all Milnor invariants of the link with $r\leq 2$ vanish.

The Fourth East Asian School of Knots and Related Topics
Y.Y. (Thanks to the staffs of 1st, 2nd, 3rd of this School)