Turaev 氏の連続講義

数理解析研究所客員教授の Vladimir Turaev 氏による連続講義を 下記のようにおこないます。

日時:2006年 2月 22日(水)〜24日(金)、各日とも 14時〜17時

場所:京都大学 数理解析研究所 115号室

講師:Vladimir Turaev 氏 (CNRS - Louis Pasteur University, Strasbourg / 数理解析研究所)

Title: Topology of words

Abstract: Words are finite sequences of letters from a fixed alphabet. We study words using ideas and techniques from low-dimensional topology. The relevance of topology is suggested by the well-known connection to closed plane curves, first pointed out by Gauss, and also by the phenomenon of linking of letters in words. A prototypical example is provided by the words $abab$ and $aabb$. The letters $a,b$ are obviously linked in the first word and unlinked in the second one. This phenomenon is similar to the linking of geometric objects, for instance knots in Euclidean 3-space. The study of words by topological methods includes as special cases a study of closed cuves and link diagrams on oriented surfaces. A number of standard link invariants, say the link quandle, the Kauffman bracket polynomial, the genus, naturally appear in this setting although in a modified form.

1. Words and etale words.
2. Nanowords.
3. Homotopy of nanowords.
4. Curves and links on surfaces as nanowords.
5. Self-linking and coverings of nanowords.
6. Linking forms and linking pairings of nanowords.
7. Analysis litterae: homotopy classification of words of length $\leq 5$.
8. Further invariants of nanowords (colorings, modules, polynomials).
9. Keis of nanowords.
10. Cobordism of nanowords.

1. V. Turaev, Topology of words, math.CO/0503683.
2. V. Turaev, Knots and words, math.GT/0506390.
3. V. Turaev, Cobordism of words, math.CO/0511513.

連絡先:大槻 知忠 (京大数理研、tomotadakurims.kyoto-u.ac.jp)