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On numerical invariants for knots in the solid torus

Khaled Bataineh (2015)

Open Mathematics

We define some new numerical invariants for knots with zero winding number in the solid torus. These invariants explore some geometric features of knots embedded in the solid torus. We characterize these invariants and interpret them on the level of the knot projection. We also find some relations among some of these invariants. Moreover, we give lower bounds for some of these invariants using Vassiliev invariants of type one. We connect our invariants to the bridge number in the solid torus. We...

On oriented vector bundles over CW-complexes of dimension 6 and 7

Martin Čadek, Jiří Vanžura (1992)

Commentationes Mathematicae Universitatis Carolinae

Necessary and sufficient conditions for the existence of n -dimensional oriented vector bundles ( n = 3 , 4 , 5 ) over CW-complexes of dimension 7 with prescribed Stiefel-Whitney classes w 2 = 0 , w 4 and Pontrjagin class p 1 are found. As a consequence some results on the span of 6 and 7-dimensional oriented vector bundles are given in terms of characteristic classes.

On parabolic Whittaker functions II

Sergey Oblezin (2012)

Open Mathematics

We propose a Givental-type stationary phase integral representation for the restricted Grm,N-Whittaker function, which is expected to describe the (S 1×U N)-equivariant Gromov-Witten invariants of the Grassmann variety Grm,N. Our key tool is a generalization of the Whittaker model for principal series U(gl N)-modules, and its realization in the space of functions of totally positive unipotent matrices. In particular, our construction involves a representation theoretic derivation of the Batyrev-Ciocan-Fontanine-Kim-van...

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