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Hokkaido University Preprint Series in Mathematics >
KHOVANOV HOMOLOGY AND WORDS
| Title: | KHOVANOV HOMOLOGY AND WORDS |
| Authors: | Fukunaga, Tomonori Browse this author | | Ito, Noboru Browse this author |
| Keywords: | Turaev's homotopy theory of phrases | | categorification | | Jones polynomial | | homotopy invariants of phrases |
| Issue Date: | 1-Jul-2009 |
| Publisher: | Department of Mathematics, Hokkaido University |
| Journal Title: | Hokkaido University Preprint Series in Mathematics |
| Volume: | 943 |
| Start Page: | 1 |
| End Page: | 52 |
| Abstract: | In word and phrase theory of Turaev, we interpret links or virtual inks as equivalences of phrases over an alphabet consisting four letters. V. Turaev onstructed a version of the Jones polynomial for phrases. We study the ell-definedness of the Jones polynomial for phrases in word theory. On the ther hand, M. Khovanov introduced a collection of homology groups which is strictly stronger link invariant than the Jones polynomial and O. Viro reconstructed hese Khovanov homology groups. We construct phrase invariants as the omology groups of certain chain complexes for phrases where the coefficients of he Jones polynomial are the Euler characteristics of these complexes using the iro’s method of Khovanov theory. The invariance of these homology groups is howed in only terminology of Turaev’s theory of phrases. Moreover, we apply he homology groups to getting invariants for an other type of phrases over an lphabet consisting any letters. |
| Type: | bulletin (article) |
| URI: | http://hdl.handle.net/2115/69750 |
| Appears in Collections: | 理学院・理学研究院 (Graduate School of Science / Faculty of Science) > Hokkaido University Preprint Series in Mathematics
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Submitter: 数学紀要登録作業用
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