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Signature of rotors

Mieczysław K. Dąbkowski, Makiko Ishiwata, Józef H. Przytycki, Akira Yasuhara (2004)

Fundamenta Mathematicae

Rotors were introduced as a generalization of mutation by Anstee, Przytycki and Rolfsen in 1987. In this paper we show that the Tristram-Levine signature is preserved by orientation-preserving rotations. Moreover, we show that any link invariant obtained from the characteristic polynomial of the Goeritz matrix, including the Murasugi-Trotter signature, is not changed by rotations. In 2001, P. Traczyk showed that the Conway polynomials of any pair of orientation-preserving rotants coincide. We show...

Simple framed curve singularities

Victor Goryunov, Gabor Lippner (2008)

Banach Center Publications

We obtain a complete list of simple framed curve singularities in ℂ² and ℂ³ up to the framed equivalence. We also find all the adjacencies between simple framed curves.

Singular Hecke algebras, Markov traces, and HOMFLY-type invariants

Luis Paris, Loïc Rabenda (2008)

Annales de l’institut Fourier

We define the singular Hecke algebra ℋ ( S B n ) as the quotient of the singular braid monoid algebra ℂ ( q ) [ S B n ] by the Hecke relations σ k 2 = ( q - 1 ) σ k + q , 1 ≤ k ≤ n - 1 . We define the notion of Markov trace in this context, fixing the number d of singular points, and we prove that a Markov trace determines an invariant on the links with d singular points which satisfies some skein relation. Let TR d denote the set of Markov traces with d singular points. This is a ℂ ( q , z ) -vector space. Our main result is that TR d is of dimension d + 1 . This result is completed...

Singular open book structures from real mappings

Raimundo Araújo dos Santos, Ying Chen, Mihai Tibăr (2013)

Open Mathematics

We define open book structures with singular bindings. Starting with an extension of Milnor’s results on local fibrations for germs with nonisolated singularity, we find classes of genuine real analytic mappings which yield such open book structures.

Currently displaying 61 – 80 of 445