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
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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
（先にアナウンスしました講義室が変更になりました）
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.
Contents.
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.
Bibliography:
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、tomotada
kurims.kyoto-u.ac.jp）