TY - JOUR

T1 - Quandle cocycles from invariant theory

AU - Nosaka, Takefumi

N1 - Funding Information:
I am grateful to J. Scott Carter for many discussions on -families of quandles during a visit to the University of South Alabama. I also thank Masahide Iwakiri, Kengo Kishimoto, Kanako Oshiro, and Masahico Saito for useful comments. I am particularly grateful to Atsushi Ishii for valuable advice and discussions. This work was partly supported by a JSPS Research Fellowship for Young Scientists .

PY - 2013/10/1

Y1 - 2013/10/1

N2 - Let G be a group. Any G-module M has an algebraic structure called a G-family of Alexander quandles. Given a 2-cocycle of a cohomology associated with this G-family, topological invariants of (handlebody) knots in the 3-sphere are defined. We develop a simple algorithm to algebraically construct n-cocycles of this G-family from G-invariant group n-cocycles of the abelian group M. We present many examples of 2-cocycles of these G-families using facts from (modular) invariant theory.

AB - Let G be a group. Any G-module M has an algebraic structure called a G-family of Alexander quandles. Given a 2-cocycle of a cohomology associated with this G-family, topological invariants of (handlebody) knots in the 3-sphere are defined. We develop a simple algorithm to algebraically construct n-cocycles of this G-family from G-invariant group n-cocycles of the abelian group M. We present many examples of 2-cocycles of these G-families using facts from (modular) invariant theory.

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U2 - 10.1016/j.aim.2013.05.022

DO - 10.1016/j.aim.2013.05.022

M3 - Article

AN - SCOPUS:84880641671

VL - 245

SP - 423

EP - 438

JO - Advances in Mathematics

JF - Advances in Mathematics

SN - 0001-8708

ER -