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Heegaard splittings of the pair of solid torus and the core loop.

Chuichiro Hayashi, Koya Shimokawa (2001)

Revista Matemática Complutense

We show that any Heegaard splitting of the pair of the solid torus (≅D2xS1) and its core loop (an interior point xS1) is standard, using the notion of Heegaard splittings of pairs of 3-manifolds and properly imbedded graphs, which is defined in this paper.

High-dimensional knots corresponding to the fractional Fibonacci groups

Andrzej Szczepański, Andreĭ Vesnin (1999)

Fundamenta Mathematicae

We prove that the natural HNN-extensions of the fractional Fibonacci groups are the fundamental groups of high-dimensional knot complements. We also give some characterization and interpretation of these knots. In particular we show that some of them are 2-knots.

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 , ) .

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