The current quantity grew out of the Heidelberg Knot concept Semester, geared up by means of the editors in iciness 2008/09 at Heidelberg college. The contributed papers deliver the reader modern at the at the moment so much actively pursued components of mathematical knot conception and its functions in mathematical physics and telephone biology. either unique study and survey articles are awarded; various illustrations aid the textual content. The publication can be of serious curiosity to researchers in topology, geometry, and mathematical physics, graduate scholars focusing on knot idea, and phone biologists attracted to the topology of DNA strands.
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Additional info for The Mathematics of Knots: Theory and Application (Contributions in Mathematical and Computational Sciences, Volume 1)
Computing twisted signatures and L-classes of non-Witt spaces. Proc. Lond. Math. Soc. : Topological Invariants of Stratified Spaces. : The signature of partially defined local coefficient systems. J. Knot Theory Ramif. : Computing twisted signatures and L-classes of stratified spaces. Math. Ann. : Singular spaces, characteristic classes, and intersection homology. Ann. Math. 134, 325–374 (1991) 30 M. Banagl et al. : Classification of simple knots by Blanchfield duality. Bull. Am. Math. Soc. : Les nœuds de dimensions supérieures.
A multi-variable polynomial invariant for virtual knots and links. J. Knot Theory Ramif. 17(11), 1311–1326 (2008) Chapter 3 A Survey of Twisted Alexander Polynomials Stefan Friedl and Stefano Vidussi Abstract We give a short introduction to the theory of twisted Alexander polynomials of a 3-manifold associated to a representation of its fundamental group. We summarize their formal properties and we explain their relationship to twisted Reidemeister torsion. We then give a survey of the many applications of twisted invariants to the study of topological problems.
R[t1±1 , . . , tm 5. Finally given a link L we also drop the representation from the notation when the representation is the trivial representation to GL(1, Z). With all these conventions, given a knot K ⊂ S 3 , the polynomial Z[t ±1 ] is just the ordinary Alexander polynomial. 5 Computation of Twisted Alexander Polynomials Let N be a 3-manifold with empty or toroidal boundary, α : π1 (N ) → GL(k, R[F ]) a representation with R a Noetherian UFD and F a free abelian group. Given a finite presentation for π1 (N ) the polynomials αN,1 ∈ R[F ] and αN,0 ∈ R[F ] can be computed efficiently using Fox calculus (cf.
The Mathematics of Knots: Theory and Application (Contributions in Mathematical and Computational Sciences, Volume 1)