Related papers: Torsion Invariants for Families
We compute the invariants for a class of knots and links in arbitrary representations in $S^3/\mathbb{Z}_p$ in the large $k$ (level), large $N$ (rank) limit, keeping $N/(k+N)=\lambda$ fixed, in $U(N)$ and $Sp(N)$ Chern-Simons theories.…
In this article, we use two different approaches -- one algebraic and the other analytic -- to study the variation of Iwasawa invariants of rational elliptic curves in some quadratic twist families. The analytic approach involves a thorough…
Higher-order gravity models have been recently the subject of much attention in the context of cosmic acceleration. These models are derived by adding various curvature invariants to the Einstein-Hilbert action. Several studies showed that…
Comparing invariants from both topological and geometric perspectives is a key focus in index theorem. This paper compares higher analytic and topological torsions and establishes a version of the higher Cheeger-M\"uller/Bismut-Zhang…
I adapt a recently introduced method for integrating over the unitary group (S. Aubert and C.S. Lam, J.Math.Phys. 44, 6112-6131 (2003)) to the orthogonal group. I derive explicit formulas for a number of one, two and three-vector integrals,…
We study noncommutative deformations of Yang-Mills theories and show that these theories admit a infinite, continuous family of twisted star-gauge invariances. This family interpolates continuously between star-gauge and twisted gauge…
Two new invariants that are closely related to Milnor's curvature-torsion invariant are introduced. The first, the spiral index of a knot, captures the minimum number of maxima among all knot projections that are free of inflection points.…
This article studies left-invariant Hermitian structures on Lie groups with two-dimensional commutator subgroups. We provide an explicit classification for two specific types of such structures, which we designate as Type I and Type II.…
A new counterpart of Bessel's inequality for orthornormal families in real or complex inner product spaces is obtained. Applications for some Gruss type results are also provided.
Torus knots are an important family of knots about which much is understood; invariants of torus knots often exhibit nice formulas, making them convenient and fundamental building blocks for examples in knot theory. Spiral knots, defined…
Considering a family of upper frequently hypercyclic operators we care about the existence of vectors which are upper frequently hypercyclic for any operator of this family. We establish sufficient conditions for a family of operators to…
The path integral generalization of the Casson invariant as developed by Rozansky and Witten is investigated. The path integral for various three manifolds is explicitly evaluated. A new class of topological observables is introduced that…
In this paper, we first introduce twisted Rota-Baxter families on Lie-Yamaguti algebras indexed by a commutative semigroup $\Omega$. Then, we study NS-Lie-Yamaguti family algebras as the underlying structures of twisted Rota-Baxter…
We introduce a generalization of the Dijkgraaf-Witten invariants for cusped or compact oriented 3-manifolds. We show that the generalized DW invariants distinguish some pairs of cusped hyperbolic 3-manifolds with the same hyperbolic volumes…
This is the draft of lecture notes for Phd students in Sichuan University. In this notes we expand Li-Ruan's paper with much more detailed explanations and calculations.
Withdrawn and replaced by two related manuscripts: (1) "Stabilization in the braid groups I:MTWS", published in Geometry and Topology Volume 10 (2006), 413-540, arXiv:math.GT/0310279, and (2) "Stabilization in the braid groups II:…
This is a compilation of three separated studies. The main part (Part 3) deals with a unified Picard-Vessiot theory including Picard-Vessiot theories of differential and difference equations. Changes: [v1 -> v2] Corrected descriptions on…
This paper concentrates on analyzing Witten deformation for a family of non-Morse functions parameterized by $T\in \mathbb{R}_+$, resulting in a novel, purely analytic proof of the gluing formula for analytic torsions in complete generality…
We show how general principles of symmetry in quantum mechanics lead to twisted notions of a group representation. This framework generalizes both the classical 3-fold way of real/complex/quaternionic representations as well as a…
A formula is given for the Seiberg-Witten invariants of a 4-manifold that is cut along certain kinds of 3-dimensional tori. The formula involves a Seiberg-Witten invariant for each of the resulting pieces.