East Asia Knot School 4: Abstract of Plenary Talks

Abstract of Plenary Talks

Plenary Talks China Japan+ Korea Poster TalkSchedule

Title : Slicing iterated Bing doubles [PDF]
Speaker : Jae Choon CHA (POSTECH)
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Title : Computing the Nielsen number on a graph --- a survey [PDF]
Speaker : Boju Jiang (Peking University)
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Title : Prime knots with arc index up to 11 and an upper bound of arc index for non-alternating knots [PDF]
Speaker : Gyo Taek JIN (KAIST)
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Title : On the Alexander polynomials of alternating knots of genus two [PDF]
Speaker : In Dae Jong (Osaka City University)
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Title : Graph braid groups and right angled Artin groups [PDF]
Speaker : Ki Hyoung KO (KAIST)
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Title : Applications of braid group representations to dynamical systems [PDF]
Speaker : Takashi Matsuoka (Naruto University of Teacher Education)
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Title : On the signature cocycle and related invariants of 3-manifolds [PDF]
Speaker : Takayuki Morifuji (Tokyo Univ. Agri. & Tech.)
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Title : Dynamics of gradient flows in the non-transversal Morse theory [PDF]
Speaker : Andrei Pajitnov (Universite de Nantes)
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Title : On the Heegaard genus of knot exteriors
Speaker : Yo'av Rieck (the University of Arkansas) --- (joint with Tsuyoshi Kobayashi)
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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 : On embedding all $n$-manifolds into a single $(n+1)$-manifold [PDF]
Speaker : Jiangang Yao (UC Berkeley)
Abstract :

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