Related papers: Applications of another characterization of betaN\…

We present the construction of a Chern character in cyclic cohomology, involving an arbitrary number of associative algebras in contravariant or covariant position. This is a generalization of the bivariant Chern character for bornological…

We introduce Chern degree functions for complexes of coherent sheaves on a polarized surface, which encode information given by stability conditions on the boundary of the $(\alpha, \beta)$-plane. We prove that these functions extend to…

The $CP^N$ model in three euclidean dimensions is studied in the presence of a Chern-Simons term using the $1/N$ expansion. The $\beta$-function for the CS coefficient $\theta$ is found to be zero to order $1/N$ in the unbroken phase by an…

The fundamental notion of non-abelian generalized cohomology gained recognition in algebraic topology as the non-abelian Poincar\'e-dual to "factorization homology", and in theoretical physics as providing flux-quantization for non-linear…

Notes for some talks given at the seminar on characteristic classes at NTNU in autumn 2006. In the paper a proof of the existence of a Chern-character from complex K-theory to any cohomology theory with values in graded Q-algebras is given.…

In this notes we classify toric Fano 4-folds having positive second Chern Character.

The main result is a submetric characterization of the class of Banach spaces admitting an equivalent norm with Rolewicz's property ($\beta$). As applications we prove that up to renorming, property ($\beta$) is stable under coarse…

The Birkhoff--Kakutani Theorem asserts that a topological group is metrizable if and only if it has countable character. We develop and apply tools for the estimation of the character for a wide class of nonmetrizable topological groups. We…

We give a new formula for the Chern-Schwartz-MacPherson class of a hypersurface in a nonsigular compact complex analytic variety. In particular this formula generalizes our previous result on the Euler characteristic of such a hypersurface.…

We describe the second integral cohomology group of a surface bundle as the group of Chern classes of fiberwise holomorphic complex line bundles and use this to obtain information on this group.

A topological model in three dimensions is proposed. It combines the Chern-Simons action with a BFK-model which was investigated recently by the authors of hep-th/9906146. The finiteness of the model to all orders of perturbation theory is…

Topological property in a spinning system should be directly associated with its wavefunction. A complete decomposition formula of SU(2) gauge potential in terms of spinning wavefunction is established rigorously. Based on the $\phi…

We introduce a Hamiltonian for fermions on a lattice and prove a theorem regarding its topological properties. We identify the topological criterion as a $\mathbb{Z}_2-$ topological invariant $p(\textbf{k})$ (the Pfaffian polynomial). The…

Let X be a variety over a field of characteristic 0. Given a vector bundle E on X we construct Chern forms c_{i}(E;\nabla) in \Gamma(X, \cal{A}^{2i}_{X}). Here \cal{A}^{.}_{X} is the sheaf Beilinson adeles and \nabla is an adelic…

Regarding the Skyrme-Faddeev model on $\mathbb R^3$ as a $\mathbb C \mathbb P^1$ sigma model, we propose $\mathbb C \mathbb P^n$ sigma models on $\mathbb R^{2n+1}$ as generalisations which may support finite energy Hopfion solutions in…

We deduce Paley-Wiener results in the Bargmann setting, which give characterisations of Pilipovi{\'c} spaces of low orders, extending the characterisation of a Gr{\"o}chenig test function space, deduced earlier by the third author.

Under the assumption that the continuum c is a regular cardinal, we prove the existence and uniqueness of a Boolean algebra B of size c defined by sharing the main structural properties that P(N)/fin has under CH and in the aleph2-Cohen…

A basic result in the theory of holomorphic functions of several complex variables is the following special case of the work of H. Cartan on the sheaf cohomology on Stein domains ([10], or see [14] or [16] for more modern treatments).

Coherent sheaves on general complex manifolds do not necessarily have resolutions by finite complexes of vector bundles. However D. Toledo and Y.L.L. Tong showed that one can resolve coherent sheaves by objects analogous to chain complexes…

Topology ultimately unveils the roots of the perfect quantization observed in complex systems. The 2D quantum Hall effect is the celebrated archetype. Remarkably, topology can manifest itself even in higher-dimensional spaces in which…