Related papers: Torsion, as a function on the space of representat…

Topological invariants such as winding numbers and linking numbers appear as charges of topological solitons in diverse nonlinear physical systems described by a unit vector field defined on two and three dimensional manifolds. While the…

We define an invariant of graphs embedded in a three-manifold and a partition function for 2-complexes embedded in a triangulated four-manifold by specifying the values of variables in the Turaev-Viro and Crane-Yetter state sum models. In…

In this paper we define a Poincar\'e-Reidemeister scalar product on the determinant line of the cohomology of any flat vector bundle over a closed orientable odd-dimensional manifold. It is a combinatorial "torsion-type" invariant which…

Recently, Cappell and Miller extended the classical construction of the analytic torsion for de Rham complexes to coupling with an arbitrary flat bundle and the holomorphic torsion for $\bar{\partial}$-complexes to coupling with an…

In this paper, we extend Su-Zhang's Cheeger-Mueller type theorem for symmetric bilinear torsions to manifolds with boundary in the case that the Riemannian metric and the non-degenerate symmetric bilinear form are of product structure near…

We consider harmonic sections of a bundle over the complement of a codimension 2 submanifold in a Riemannian manifold, which can be thought of as multivalued harmonic functions. We prove a result to the effect that these are stable under…

There is a need in general relativity for a consistent and useful mathematical theory defining the multiplication of tensor distributions in a geometric (diffeomorphism invariant) way. Significant progress has been made through the concept…

We investigate the random dynamics of rational maps on the Riemann sphere and the dynamics of semigroups of rational maps on the Riemann sphere. We show that regarding random complex dynamics of polynomials, in most cases, the chaos of the…

We derive a class of variational functionals which arise naturally in conformal geometry. In the special case when the Riemannian manifold is locally conformal flat, the functional coincides with the well studied functional which is the…

The definition of a non-trivial space of generalized functions of a complex variable allowing to consider derivatives of continuous functions is a non-obvious task, e.g. because of Morera theorem, because distributional Cauchy-Riemann…

We give a dynamical description, in terms of a Weil-type zeta function, to the holomorphic torsion with coefficients for certain compact Hermitian locally symmetric manifolds, whose connected group G of isometries of the universal cover has…

We prove that the Riemannian geometry of almost K\"ahler manifolds can be expressed in terms of the Poisson algebra of smooth functions on the manifold. Subsequently, K\"ahler-Poisson algebras are introduced, and it is shown that a…

We study two sorts of actions on the space of conjugacy classes of irreducible $SU_2$-representations of a knot group. One of them is an involution which comes from the algebraic structure of $SU_2$ and the other is the action by the outer…

Given a closed symplectic 4-manifold $(X,\omega)$, we define a twisted version of the Gromov-Taubes invariants for $(X,\omega)$, where the twisting coefficients are induced by the choice of a surface bundle over $X$. Given a fibered…

One constructs new operations of pull-back and push-forward on valuations on manifolds with respect to submersions and immersions. A general Radon type transform on valuations is introduced using these operations and the product on…

For a Morse function on a closed orientable Riemannian manifold one introduces the {\it virtually small spectral package} an analytic object consisting of a finite number of analytic quantities derived from the pair, {\it Riemannian metric,…

For a smooth function on a smooth manifold of a suitable class, the space of all connected components of preimages is the graph and called the {\it Reeb graph}. Reeb graphs are fundamental tools in the algebraic and differential topological…

We study analytic torsion and eta like invariants on CR contact manifolds of any dimension admitting a circle transverse action, and equipped with a unitary representation. We show that, when defined using the spectrum of relevant operators…

We characterize isometric actions whose principal orbits are hypersurfaces through the existence of a linear connection satisfying a set of covariant equations in the same spirit as the Ambrose-Singer Theorem for homogeneous space. These…

We define transalgebraic functions on a compact Riemann surface as meromorphic functions except at a finite number of punctures where they have finite order exponential singularities. This transalgebraic class is a topological…