Related papers: Absolute torsion

It is well known that a rigid motion of the Euclidean plane can be written as the composition of at most three reflections. It is perhaps not so widely known that a similar result holds for Euclidean space in any number of dimensions. The…

The presented paper is devoted to study the curvature and torsion of slant Frenet curves in 3-dimensional normal almost paracontact metric manifolds. Moreover, in this class of manifolds, properties of non- Frenet slant curves (with null…

Geodesically complete affine manifolds are quotients of the Euclidean space through a properly discontinuous action of a subgroup of affine Euclidean transformations. An equivalent definition is that the tangent bundle of such a manifold…

We review the Reidemeister torsion, Ray-Singer's analytic torsion and the Cheeger-M"uller theorem. We describe the analytic torsion of the de Rham complex twisted by a flux form introduced by the current authors and recall its properties.…

The main goal of this thesis is to develop the integration theory of curved homotopy Lie algebras. In the first chapter, we develop the operadic calculus needed: we encode non-necessarily conilpotent coalgebras with operads and introduce…

We consider non-infinitesimal deformations of G2-structures on 7-dimensional manifolds and derive an exact expression for the torsion of the deformed G2-structure. We then specialize to a case when the deformation is defined by a vector v…

Twisted torus knots are a generalization of torus knots, obtained by introducing additional full twists to adjacent strands of the torus knots. In this article, we present an explicit formula for the Alexander polynomial of twisted torus…

In the case of smooth manifolds, we use Forman's discrete Morse theory to realize combinatorially any Thom-Smale complex coming from a smooth Morse function by a couple triangulation-discrete Morse function. As an application, we prove that…

In this paper we define the adjoint Reidemeister torsion as a differential form on the character variety of a compact oriented 3-manifold with toral boundary, and prove it defines a regular volume form. Then we show that the torsion form…

We investigate the holonomy group of a linear metric connection with skew-symmetric torsion. In case of the euclidian space and a constant torsion form this group is always semisimple. It does not preserve any non-degenerated 2-form or any…

We express the signature modulo 4 of a closed, oriented, $4k$-dimensional $PL$ manifold as a linear combination of its Euler characteristic and the new absolute torsion invariant defined in Korzeniewski [11]. Let $F \to E \to B$ be a $PL$…

In the previous article "Refined Analytic Torsion on Manifolds with Boundary" we have presented a construction of refined analytic torsion in the spirit of Braverman and Kappeler, which does apply to compact manifolds with and without…

A detailed analysis of the remainder obtained by truncating the Euler series up to the $n$th-order term is presented. In particular, by using an approach recently proposed by Weniger, asymptotic expansions of the remainder, both in inverse…

Let $M_n$ be a homology 3-sphere obtained by $\frac1n$-Dehn surgery along a $(p,q)$-torus knot. We consider a polynomial $\sigma_{(p,q,n)}(t)$ whose zeros are the inverses of the Reideimeister torsion of $M_n$ for…

Generic absoluteness is the phenomenon that certain truths in the set-theoretic universe remain stable under forcing expansions. A classical result by Kripke asserts that every complete Boolean algebra completely embeds into a countably…

For a knot $K$ in a homology $3$-sphere $\Sigma$, let $M$ be the result of $2/q$-surgery on $K$, and let $X$ be the universal abelian covering of $M$. Our first theorem is that if the first homology of $X$ is finite cyclic and $M$ is a…

We introduce $L^2$-Alexander torsions for 3-manifolds, which can be viewed as a generalization of the $L^2$-Alexander polynomial of Li--Zhang. We state the $L^2$-Alexander torsions for graph manifolds and we partially compute them for…

For an acyclic representation of the fundamental group of a compact oriented odd-dimensional manifold, which is close enough to a unitary representation, we define a refinement of the Ray-Singer torsion associated to this representation.…

The problem of finding perfect Euler cuboids or proving their non-existence is an old unsolved problem in mathematics. The second cuboid conjecture is one of the three propositions suggested as intermediate stages in proving the…

In this paper, we show that the Euler characteristic of an even dimensional closed projectively flat manifold is equal to the total measure which is induced from a probability Borel measure on RP^n invariant under the holonomy action, and…