Enhancements of rack counting invariants via dynamical cocycles

Alissa S. Crans; Sam Nelson; Aparna Sarkar

Enhancements of rack counting invariants via dynamical cocycles

Alissa S. Crans
, Sam Nelson
, Aparna Sarkar

Mathematics, Statistics and Data Science

Claremont McKenna College
Pomona College

Research output: Contribution to journal › Article › peer-review

Abstract

We introduce the notion of N-reduced dynamical cocycles and use these objects to define enhancements of the rack counting invariant for classical and virtual knots and links. We provide examples to show that the new invariants are not determined by the rack counting invariant, the Jones polynomial or the generalized Alexander polynomial.

Original language	English
Pages (from-to)	337-351
Journal	New York Journal of Mathematics
Volume	18
State	Published - 2012

Keywords

Dynamical cocycles
enhancements of counting invariants
co- cycle invariants

Disciplines

Algebra

Access to Document

https://digitalcommons.lmu.edu/math_fac/58

Cite this

@article{a21920d640364c88b52d89c751cfd4bf,

title = "Enhancements of rack counting invariants via dynamical cocycles",

abstract = " We introduce the notion of N-reduced dynamical cocycles and use these objects to define enhancements of the rack counting invariant for classical and virtual knots and links. We provide examples to show that the new invariants are not determined by the rack counting invariant, the Jones polynomial or the generalized Alexander polynomial.",

keywords = "Dynamical cocycles, enhancements of counting invariants, co- cycle invariants",

author = "Crans, \{Alissa S.\} and Sam Nelson and Aparna Sarkar",

note = "Crans, A.; Nelson, S.; and Sarkar, A. “Enhancements of the rack counting invariant via N-reduced dynamical cocycles.” New York Journal of Mathematics, Vol. 18 (2012): 337 – 351.",

year = "2012",

language = "English",

volume = "18",

pages = "337--351",

journal = "New York Journal of Mathematics",

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T1 - Enhancements of rack counting invariants via dynamical cocycles

AU - Crans, Alissa S.

AU - Nelson, Sam

AU - Sarkar, Aparna

N1 - Crans, A.; Nelson, S.; and Sarkar, A. “Enhancements of the rack counting invariant via N-reduced dynamical cocycles.” New York Journal of Mathematics, Vol. 18 (2012): 337 – 351.

PY - 2012

Y1 - 2012

N2 - We introduce the notion of N-reduced dynamical cocycles and use these objects to define enhancements of the rack counting invariant for classical and virtual knots and links. We provide examples to show that the new invariants are not determined by the rack counting invariant, the Jones polynomial or the generalized Alexander polynomial.

AB - We introduce the notion of N-reduced dynamical cocycles and use these objects to define enhancements of the rack counting invariant for classical and virtual knots and links. We provide examples to show that the new invariants are not determined by the rack counting invariant, the Jones polynomial or the generalized Alexander polynomial.

KW - Dynamical cocycles

KW - enhancements of counting invariants

KW - co- cycle invariants

M3 - Article

VL - 18

SP - 337

EP - 351

JO - New York Journal of Mathematics

JF - New York Journal of Mathematics

ER -