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Tuesday Seminar on Topology
Seminar information archive ～04/25｜Next seminar｜Future seminars 04/26～
| Date, time & place | Tuesday 17:00 - 18:30 056Room #056 (Graduate School of Math. Sci. Bldg.) |
|---|---|
| Organizer(s) | KAWAZUMI Nariya, KITAYAMA Takahiro, SAKASAI Takuya |
2010/06/29
16:30-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)
Takahiro Kitayama (The University of Tokyo)
Non-commutative Reidemeister torsion and Morse-Novikov theory (JAPANESE)
Takahiro Kitayama (The University of Tokyo)
Non-commutative Reidemeister torsion and Morse-Novikov theory (JAPANESE)
[ Abstract ]
For a circle-valued Morse function of a closed oriented manifold, we
show that Reidemeister torsion over a non-commutative formal Laurent
polynomial ring equals the product of a certain non-commutative
Lefschetz-type zeta function and the algebraic torsion of the Novikov
complex over the ring. This gives a generalization of the results of
Hutchings-Lee and Pazhitnov on abelian coefficients. As a consequence we
obtain Morse theoretical and dynamical descriptions of the higher-order
Alexander polynomials.
For a circle-valued Morse function of a closed oriented manifold, we
show that Reidemeister torsion over a non-commutative formal Laurent
polynomial ring equals the product of a certain non-commutative
Lefschetz-type zeta function and the algebraic torsion of the Novikov
complex over the ring. This gives a generalization of the results of
Hutchings-Lee and Pazhitnov on abelian coefficients. As a consequence we
obtain Morse theoretical and dynamical descriptions of the higher-order
Alexander polynomials.
