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Displaying 181 – 200 of 252

Resurgence of the Kontsevich-Zagier series

Ovidiu Costin, Stavros Garoufalidis (2011)

Annales de l’institut Fourier

The paper is concerned with the resurgence of the Kontsevich-Zagier series $f (q) = \sum_{n = 0}^{\infty} (1 - q) \dots (1 - q^{n})$ We give an explicit formula for the Borel transform of the power series when $q = e^{1 / x}$ from which its analytic continuation, its singularities (all on the positive real axis) and the local monodromy can be manifestly determined. We also give two formulas (one involving the Dedekind eta function, and another involving the complex error function) for the right, left and median summation of the Borel transform. We also prove that the...

Ribbon knots of 1-fusion, the Jones polynomial, and the Casson-Walker invariant.

Yoko Mizuma (2005)

Revista Matemática Complutense

We give an explicit formula for the Casson-Walker invariant of double branched covers of S3 branched along ribbon knots of 1-fusion.

Rounding corners of polygons and the embedded contact homology of $T^{3}$ .

Hutchings, Michael, Sullivan, Michael (2006)

Geometry & Topology

Seiberg-Witten invariants and surface singularities.

Némethi, András, Nicolaescu, Liviu I. (2002)

Geometry & Topology

Shadow world evaluation of the Yang-Mills measure.

Frohman, Charles, Kania-Bartoszynska, Joanna (2004)

Algebraic & Geometric Topology

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...

Signed ordered knotlike quandle presentations.

Nelson, Sam (2005)

Algebraic & Geometric Topology

Skein algebras of the solid torus and symmetric spatial graphs

Nafaa Chbili (2006)

Fundamenta Mathematicae

We use the topological invariant of spatial graphs introduced by S. Yamada to find necessary conditions for a spatial graph to be periodic with a prime period. The proof of the main result is based on computing the Yamada skein algebra of the solid torus and then proving that it injects into the Kauffman bracket skein algebra of the solid torus.