$BF|;~!'(B2006$BG/(B 2$B7n(B 22$BF|!J?e!K!A(B24$BF|!J6b!K!"3FF|$H$b(B 14$B;~!A(B17$B;~(B
$B>l=j!'5~ETBg3X(B $B?tM}2r@O8&5f=j(B 115$B9f<<(B
$B9V;U!'(BVladimir Turaev $B;a(B
$B!J(BCNRS - Louis Pasteur University, Strasbourg / $B?tM}2r@O8&5f=j!K(B
Title: Topology of words
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.
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,
2. V. Turaev, Knots and words,
3. V. Turaev, Cobordism of words,