Related papers: Reidemeister torsion for flat superconnections

We show a relationship between the non-acyclic Reidemeister torsion and a zero of the acyclic Reidemeister torsion for a lambda-regular SU(2) or SL(2, C)-representation of a knot group. Then we give a method to calculate the non-acyclic…

Using analytic torsion associated to stable bundles, we introduce zeta functions for compact Riemann surfaces. To justify the well-definedness, we analyze the degenerations of analytic torsions at the boundaries of the moduli spaces, the…

Many physical theories, including notably string theory, require non-abelian higher gauge fields defining higher holonomy. Previous approaches to such higher connections on categorified principal bundles require these to be fake flat. This…

Let T -> S be a finite flat morphism of degree two between regular integral schemes of dimension at most two (and with 2 invertible), having regular branch divisor D. We establish a bijection between Azumaya quaternion algebras on T and…

We revisit the generalized connection of Double Field Theory. We implement a procedure that allow us to re-write the Double Field Theory equations of motion in terms of geometric quantities (like generalized torsion and non-metricity…

We show that the $U(1,1)$ (super) Chern Simons theory is one loop exact. This provides a direct proof of the relation between the Alexander polynomial and analytic and Reidemeister torsion. We then proceed to compute explicitely the…

We construct supersymmetric field theories on Riemannian three-manifolds M, focusing on N=2 theories with a U(1)_R symmetry. Our approach is based on the rigid limit of new minimal supergravity in three dimensions, which couples to the…

We study the Morse theory of the Yang-Mills-Higgs functional on the space of pairs $(A,\Phi)$, where $A$ is a unitary connection on a rank 2 hermitian vector bundle over a compact Riemann surface, and $\Phi$ is a holomorphic section of $(E,…

We use a Hodge decomposition and its generalization to non-abelian flat vector bundles to calculate the partition function for abelian and non- abelian BF theories in $n$ dimensions. This enables us to provide a simple proof that the…

We define functorial isomorphisms of parallel transport along etale paths for a class of vector bundles on a p-adic curve. All bundles of degree zero whose reduction is strongly semistable belong to this class. In particular, they give rise…

We show that the absolute value at zero of the Ruelle zeta function defined by the geodesic flow coincides with the higher-dimensional Reidemeister torsion for the unit tangent bundle over a 2-dimensional hyperbolic orbifold and a…

We make evident a curvature tensor for every vector sub-bundle of an arbitrary manifold tangent bundle which reduces to the curvature tensor of an Ehresmann connection in the case of the horizontal sub-bundle of the tangent bundle to the…

In this study, we give a thorough analysis of a general affine gravity with torsion. After a brief exposition of the affine gravities considered by Eddington and Schr\"{o}dinger, we construct and analyze different affine gravities based on…

We introduce the tractor formalism from conformal geometry to the study of smooth metric measure spaces. In particular, this gives rise to a correspondence between quasi-Einstein metrics and parallel sections of certain tractor bundles. We…

Beginning with the data of a quiver Q, and its dimension vector d, we construct an algebra D_q=D_q(Mat_d(Q)), which is a flat q-deformation of the algebra of differential operators on the affine space Mat_d(Q). The algebra D_q is…

This paper aims to study the asymptotic expansion of analytic torsion forms associated with a certain series of flat bundles. We prove the existence of the full expansion and give a formula for the sub-leading term, while Bismut-Ma-Zhang…

We study the large time behavior of the optimal transportation cost towards the uniform distribution, for the occupation measure of a stationary Brownian motion on the flat torus in $d$ dimensions, where the cost of transporting a unit of…

We describe majorization between selfadjoint operators in a $\sigma$-finite II$_\infty$ factor $(\mathcal{M},\tau)$ in terms of simple spectral relations. For a diffuse abelian von Neumann subalgebra $\mathcal{A}\subset \mathcal{M}$ with…

Getzler-Jones-Petrack introduced $A_\infty$ structures on the equivariant complex for manifold $M$ with smooth $\mathbb{S}^1$ action, motivated by geometry of loop spaces. Applying Witten's deformation by Morse functions followed by…

This paper surveys recent contructions in higher Auslander--Reiten theory. We focus on those which, due to their combinatorial properties, can be regarded as higher dimensional analogues of path algebras of linearly oriented type…