New structure for orthogonal quantum group invariants

Brauer Group Invariants Associated to Orthogonal Epsilon-constants

In this paper, the theory of ε-constants associated to tame finite group actions on arithmetic surfaces is used to define a Brauer group invariant μ(X , G, V ) associated to certain symplectic motives of weight one. The relationship between this invariant and w2(π) (the Galois-theoretic invariant associated to tame covers of surfaces defined by Cassou-Noguès, Erez and Taylor) is also discussed.

Rational invariants of ternary forms under the orthogonal group

In this article we determine a generating set of rational invariants of minimal cardinality for the action of the orthogonal group O3 on the space R[x, y, z]2d of ternary forms of even degree 2d. The construction relies on two key ingredients: On one hand, the Slice Lemma allows us to reduce the problem to dermining the invariants for the action on a subspace of the finite subgroup B3 of signed...

Refined Quantum Invariants for Three-manifolds with Structure

A New Class of Rotational Invariants Using Discrete Orthogonal Moments

This paper presents a new class of Tchebichef moments in polar coordinate form, using which rotational invariants can be easily constructed. The structure of the invariants is very similar to that of Zernike and Pseudo-Zernike moments, and their computation does not involve discrete approximation of continuous integral terms. The invariants are thus very robust in the presence of image noise, a...

Knot Invariants and New Quantum Field Theory

We propose a new gauge theory of quantum electrodynamics (QED) and quantum chromodynamics (QCD) from which we derive knot invariants such as the Jones polynomial. Our approach is inspired by the work of Witten who derived knot invariants from quantum field theory based on the Chern-Simon Lagrangian. From our approach we can derive new knot invariants which extend the Jones polynomial and give a...