Noncommutative Rational Functions and Farber's Invariants of Boundary Links

Details Noncommutative Rational Functions and Farber's Invariants of Boundary Links Noncommutative Rational Functions and Farber's Invariants of Boundary Links

2000-04-17

arxiv.org/abs/math/0004112v1

Amer. Math. Soc. Transl. (2) Vol. 194, 1999

Mathematics

Geometric Topology

Latex, 11 pages

Scientific paper

In [2] M. Farber constructed invariants of m-component boundary links with values in algebra of noncommutative rational functions. In this paper we simplify his constructions and express them by using noncommutative generalizations of determinants introduced by Gelfand and Retakh. In particular, for every finite-dimensional module N over the algebra of noncommutative polynomials of m variables we construct a characteristic rational power series chi(N). If N is an algebraically closed field of arbitrary characteristic and N is semisimple, the series chi(N) determines N.

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