A+ CATEGORY SCIENTIFIC UNIT

On constructions of generalized skein modules

Volume 100 / 2014

Uwe Kaiser Banach Center Publications 100 (2014), 153-172 MSC: 57M25, 57M35, 57R42. DOI: 10.4064/bc100-0-8

Abstract

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 TQFT-modules is discussed for those generalized skein modules. Also an approach of defining skein modules from studying compressions of fields is described.

Authors

  • Uwe KaiserBoise State University
    Department of Mathematics
    1910 University Drive, Math/Geosciences Bldg.
    Boise, ID 83725-1555, USA
    e-mail

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