arXiv research

Researchers compute torsion for homology cylinders, proving it a finite-type invariant.

New formula connects surface singularity zeta function to Reidemeister-Turaev torsion.

We prove for the Reidemeister-Turaev torsion of closed oriented three-manifolds some finiteness properties in the sense of Goussarov and Habiro, that is, with respect to some cut-and-paste operations which preserve the homology type of the manifolds. In general, those properties require the manifolds to come equipped w…

Given an oriented rational homology 3-sphere M, it is known how to associate to any Spin^c-structure σon M two quadratic functions over the linking pairing. One quadratic function is derived from the reduction modulo 1 of the Reidemeister-Turaev torsion of (M,σ), while the other one can be defined using the intersectio…

We extend Turaev's theory of Euler structures and torsion invariants on 3-manifolds to the case of vector fields having generic behavior on the boundary. This allows to easily define gluings of Euler structures and to develop a completely general gluing formula for Reidemeister torsion of 3-manifolds. Lastly, we descri…

We study lens space surgeries along two different families of 2-component links, denoted by $A_{m,n}$ and $B_{p,q}$, related with the rational homology 4-ball used in J.\ Park's (generalized) rational blow down. We determine which coefficient $r$ of the knotted component of the link yields a lens space by Dehn surgery.…

This is a continuation of our paper math.AG/0111298. We prove an explicit formula for the geometric genus p_g of a quasihomogeneous isolated surface singularity in terms of the Seiberg-Witten invariant of the link and other topological data which can be read from a resolution graph of the singularity. Moreover, we also…

We formulate a very general conjecture relating the analytical invariants of a normal surface singularity to the Seiberg-Witten invariants of its link provided that the link is a rational homology sphere. As supporting evidence, we establish its validity for a large class of singularities: some rational and minimally e…

We verify the conjecture formulated in math.AG/0111298 for suspension singularities of type $g(x,y,z)= f(x,y)+z^n$, where $f$ is an irreducible plane curve singularity. More precisely, we prove that the modified Seiberg-Witten invariant of the link $M$ of $g$, associated with the canonical $spin^c$ structure, equals $-…

Monopole Floer homology connects 3-manifold invariants to Riemann surface geometry.

A linking pairing is a symetric bilinear pairing lambda: GxG --> Q/Z on a finite abelian group. The set of isomorphism classes of linking pairings is a non-cancellative monoid E under orthogonal sum, which is infinitely generated and infinitely related. We propose a new presentation of E that enables one to detect whet…

Analytic torsion and Reidemeister torsion help show exponential growth of torsion in cohomology.

Explicitly expresses torsion functions on lens spaces.

The paper compares two torsion invariants in complex vector bundles.

Analytic torsion matches Ray-Singer for specific nilmanifolds.

New spectral torsion defined for rescaled Dirac operators.

The paper examines torsions in Minkowskian product of Finsler metrics.

Study on stable torsion length in groups, showing it vanishes in crystallographic groups and providing algorithms for computation.

Inspired by the work of Boris Vertman on refined analytic torsion for manifolds with boundary, in this paper we extend the construction of the Cappell-Miller analytic torsion to manifolds with boundary. We also compare it with the refined analytic torsion on manifolds with boundary. As a byproduct of the gluing formula…

Analytic torsion studied for fibred boundary metrics, with applications to conic degeneration.

The refined analytic torsion associated to a flat vector bundle over a closed odd-dimensional manifold canonically defines a quadratic form $τ$ on the determinant line of the cohomology. Both $τ$ and the Burghelea-Haller torsion are refinements of the Ray-Singer torsion. We show that whenever the Burghelea-Haller torsi…

Classifies simply-connected pluriclosed manifolds with parallel Bismut torsion.

Hypersymplectic structures with torsion on Lie algebroids are investigated. We show that each hypersymplectic structure with torsion on a Lie algebroid determines three Nijenhuis morphisms. From a contravariant point of view, these structures are twisted Poisson structures. We prove the existence of a one-to-one corres…

Explicit formula for Reidemeister torsion of two-bridge knots.

In this paper we show that the Ray-Singer complex analytic torsion is trivial for even dimensional Calabi-Yau manifolds. Then we define the quaternionic analytic torsion for quaternionic manifolds and prove that they are metric independent. In dimension four, the quaternionic analytic torsion equals to the self-dual an…

We introduce multi-torsion, a spectral invariant generalizing Ray-Singer analytic torsion. We define multi-torsion for compact manifolds with a certain local geometric product structure that gives a bigrading on differential forms. We prove that multi-torsion is metric-independent in a suitable sense. Our definition of…

In a recent joint work with V. Turaev (cf. math.DG/9810114) we defined a new concept of combinatorial torsion which we called absolute torsion. Compared with the classical Reidemeister torsion it has the advantage of having a well-defined sign. Also, the absolute torsion is defined for arbitrary orientable flat vector …

In the Khovanov homology of links, presence of $\mathbb{Z}_2$-torsion is a very common phenomenon. Finite number of examples of knots with $\mathbb{Z}_n$-torsion for $n>2$ were also known, none for $n>8$. In this paper, we prove that there are infinite families of links whose Khovanov homology contains $\mathbb{Z}_n$-t…

Analytic torsion defined for non-compact Lie groups and discrete subgroups.

New connections found with specific torsion properties.

A nontrivial element in a group is a generalized torsion element if some nonempty finite product of its conjugates is the identity. We prove that any generalized torsion element in a free product of torsion-free groups is conjugate to a generalized torsion element in some factor group. This implies that the fundamental…

Braverman and Kappeler introduced a refinement of the Ray-Singer analytic torsion associated to a flat vector bundle over a closed odd-dimensional manifold. We study this notion and improve the Braverman-Kappeler theorem comparing the refined analytic torsion with Farber-Turaev refinement of the combinatorial torsion. …

This paper shows hyperbolic knots can have arbitrarily large torsion in knot Floer homology.

Study shows specific states produce Khovanov homology torsion.

Paper finds generalized torsions in non-bi-orderable 3-manifold groups.

The curvature properties of a specific type of 6-manifold are explored.

Study connects spectral and algebraic torsion in geometric contexts.

The abstract discusses transformations on statistical and semi-Weyl manifolds with torsion.

Study torsion and curvature in ACYT and AHKT 8-manifolds.

Study shows torsion homology growth vanishes for certain free-by-cyclic groups.

On an odd-dimensional oriented hyperbolic manifold of finite volume with strongly acyclic coefficient systems, we derive a formula relating analytic torsion with the Reidemeister torsion of the Borel-Serre compactification of the manifold. In a companion paper, this formula is used to derive exponential growth of torsi…

Study on instantons in $G_2$ and $Spin(7)$ manifolds.

Ray-Singer torsion is a mathematical concept with applications in physics.

In this text we introduce the torsion of spinor connections. In terms of the torsion we give conditions on a spinor connection to produce Killing vector fields. We relate the Bianchi type identities for the torsion of spinor connections with Jacobi identities for vector fields on supermanifolds. Furthermore, we discuss…

Analytic torsion defined for rank 2 distributions on 5-manifolds.

New hyperbolic manifolds show exponential homology torsion growth.

The paper examines $L^2$-torsion in fibration cases relaxing standard conditions.

The study explores properties of metric connections with skew torsion and their curvature identities.