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On constructions of generalized skein modules

Uwe Kaiser (2014)

Banach Center Publications

Józef Przytycki introduced skein modules of 3-manifolds and skein deformation initiating algebraic topology based on knots. We discuss the generalized skein modules of Walker, defined by fields and local relations. Some results by Przytycki are proven in a more general setting of fields defined by decorated cell-complexes in manifolds. A construction of skein theory from embedded TQFT-functors is given, and the corresponding background is developed. The possible coloring of fields by elements of...

Quelques calculs en cobordisme lagrangien

Michèle Audin (1985)

Annales de l'institut Fourier

Nous considérons les groupes de cobordisme (définis par Arnold) d’immersions lagrangiennes exactes de variétés compactes dans R 2 n . Grâce au théorème de Gromov-Lees, leur calcul est celui des groupes d’homotopie de spectres de Thom construits sur les espaces U / O (cas non-orienté, le calcul est alors dû à Smith et Stong) et U / S O (cas orienté, groupes dont nous calculons la “partie paire”, et sur la “partie impaire” desquels nous donnons des informations). Nous calculons aussi les images de ces groupes dans...

Reidemeister-type moves for surfaces in four-dimensional space

Dennis Roseman (1998)

Banach Center Publications

We consider smooth knottings of compact (not necessarily orientable) n-dimensional manifolds in n + 2 (or S n + 2 ), for the cases n=2 or n=3. In a previous paper we have generalized the notion of the Reidemeister moves of classical knot theory. In this paper we examine in more detail the above mentioned dimensions. Examples are given; in particular we examine projections of twist-spun knots. Knot moves are given which demonstrate the triviality of the 1-twist spun trefoil. Another application is a smooth...

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