Mechanical normal forms of knots and flat knots
نویسندگان
چکیده
منابع مشابه
Semiquandles and flat virtual knots
We introduce an algebraic structure we call semiquandles whose axioms are derived from flat Reidemeister moves. Finite semiquandles have associated counting invariants and enhanced invariants defined for flat virtual knots and links. We also introduce singular semiquandles and virtual singular semiquandles which define invariants of flat singular virtual knots and links. As an application, we u...
متن کاملEquilibrium shapes of flat knots.
We study the equilibrium shapes of prime and composite knots confined to two dimensions. Using scaling arguments we show that, due to self-avoiding effects, the topological details of prime knots are localized on a small portion of the larger ring polymer. Within this region, the original knot configuration can assume a hierarchy of contracted shapes, the dominating one given by just one small ...
متن کاملGroups of locally-flat disk knots and non-locally-flat sphere knots
The classical knot groups are the fundamental groups of the complements of smooth or piecewise-linear (PL) locally-flat knots. For PL knots that are not locally-flat, there is a pair of interesting groups to study: the fundamental group of the knot complement and that of the complement of the “boundary knot” that occurs around the singular set, the set of points at which the embedding is not lo...
متن کاملAn invariant of flat virtual knots
A generalization of Jaeger’s model for the HOMFLY polynomial of classical knots to flat virtual knots is given.
متن کاملAlexander polynomials of non-locally-flat knots
We generalize the classical study of Alexander polynomials of smooth or PL locally-flat knots to PL knots that are not necessarily locally-flat. We introduce three families of generalized Alexander polynomials and study their properties. For knots with point singularities, we obtain a classification of these polynomials that is complete except for one special low-dimensional case. This classifi...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Russian Journal of Mathematical Physics
سال: 2011
ISSN: 1061-9208,1555-6638
DOI: 10.1134/s1061920811020105