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Higher simple structure sets of lens spaces with the fundamental group of arbitrary order

L’udovít Balko, Tibor Macko, Martin Niepel, Tomáš Rusin (2019)

Archivum Mathematicum

Extending work of many authors we calculate the higher simple structure sets of lens spaces in the sense of surgery theory with the fundamental group of arbitrary order. As a corollary we also obtain a calculation of the simple structure sets of the products of lens spaces and spheres of dimension grater or equal to 3 .

Hochschild cohomology and quantization of Poisson structures

Grabowski, Janusz (1994)

Proceedings of the Winter School "Geometry and Physics"

It is well-known that the question of existence of a star product on a Poisson manifold N is open and only some partial results are known [see the author, J. Geom. Phys. 9, No. 1, 45-73 (1992; Zbl 0761.16012)].In the paper under review, the author proves the existence of the star products for the Poisson structures P of the following type P = X Y with [ X , Y ] = u X + v Y , for some u , v C ( N , ) .

Hodge–type structures as link invariants

Maciej Borodzik, András Némethi (2013)

Annales de l’institut Fourier

Based on some analogies with the Hodge theory of isolated hypersurface singularities, we define Hodge–type numerical invariants of any, not necessarily algebraic, link in a three–sphere. We call them H–numbers. They contain the same amount of information as the (non degenerate part of the) real Seifert matrix. We study their basic properties, and we express the Tristram–Levine signatures and the higher order Alexander polynomial in terms of them. Motivated by singularity theory, we also introduce...

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