One day on "Invariants of homology cylinders"

A one-day workshop on "Invariants of homology cylinders" is organized the 9th of September 2019 at the IMB (Dijon), in the framework of a joint seminar CNRS-JSPS. There will be three research talks, followed by informal discussions on the subject. If you are planning to attend this meeting, please send an e-mail to gwenael.massuyeau@u-bourgogne.fr N.B. The lectures will take place in room 318 of the IMB.

• 9:45-10:45   Shunsuke TSUJI   (RIMS, Kyoto)
  
  
• 11:15-12:15   Yuta NOZAKI   (Meiji Univ., Tokyo)
  
  
• 14:15-15:15   Masatoshi SATO   (Tokyo Denki Univ.)
  
  

• Shunsuke TSUJI:   "A quantum bracket skein algebra and the total Johnson homomorphism on a homology cylinder"
  
  A homology cylinder of a compact connected surface induces an automorphism of the completion of the group ring of the fundamental group of the surface. In this talk, using a skein algebra, we give a method to compute the automorphism. In particular, we obtain an element of the completion of the Goldman Lie algebra of the surface corresponding to the automorphism.
  
  
• Yuta NOZAKI   "Abelian quotients of the Y-filtration on the homology cylinders via the LMO functor — Part I"
  
  We construct a (Z/2Z)-valued homomorphism on the graded quotient of the Y-filtration. The homomorphism restricted to the lower central series of the Torelli group is nontrivial and different from the Johnson homomorphisms. In this first talk, we explain background and the main theorem which describes the homomorphism explicitly as an operation on Jacobi diagrams. In the second talk, we give a proof of the main theorem and applications of the homomorphism. Particularly, we investigate the kernel of the surgery map constructed by Habiro and Goussarov.
  
  
• Masatoshi SATO   "Abelian quotients of the Y-filtration on the homology cylinders via the LMO functor — Part II"
  
  We construct a (Z/2Z)-valued homomorphism on the graded quotient of the Y-filtration. The homomorphism restricted to the lower central series of the Torelli group is nontrivial and different from the Johnson homomorphisms. In this first talk, we explain background and the main theorem which describes the homomorphism explicitly as an operation on Jacobi diagrams. In the second talk, we give a proof of the main theorem and applications of the homomorphism. Particularly, we investigate the kernel of the surgery map constructed by Habiro and Goussarov.