Finite type invariants for cyclic equivalence classes of nanophrases

Details Finite type invariants for cyclic equivalence classes of nanophrases Finite type invariants for cyclic equivalence classes of nanophrases

2011-12-28

arxiv.org/abs/1112.6097v3

Mathematics

Geometric Topology

15 pages, 4 figures. A acknowledgement is added, Exposition improved

Scientific paper

In this paper, we define finite type invariants for cyclic equivalence classes of nanophrases and construct the universal ones. Also, we identify the universal finite type invariant of degree 1 essentially with the linking matrix. It is known that extended Arnold's basic invariants to signed words are finite type invariants of degree 2, by Fujiwara. We give another proof of this result and show that those invariants do not provide the universal one of degree 2.

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