Related papers: Some very low-dimensional algebraic topology

We describe an interpretation of the Kervaire invariant of a Riemannian manifold of dimension $4k+2$ in terms of a holomorphic line bundle on the abelian variety $H^{2k+1}(M)\otimes R/Z$. Our results are inspired by work of Witten on the…

We introduce the concept of Bergman bundle attached to a hermitian manifold X, assuming the manifold X to be compact - although the results are local for a large part. The Bergman bundle is some sort of infinite dimensional very ample…

Possible irreducible holonomy algebras $\g\subset\osp(p,q|2m)$ of Riemannian supermanifolds under the assumption that $\g$ is a direct sum of simple Lie superalgebras of classical type and possibly of a one-dimensional center are…

We are concerned with the relaxation and existence theories of a general class of geometrical minimisation problems, with action integrals defined via differential forms over fibre bundles. We find natural algebraic and analytic conditions…

This expository paper details the theory of rank one Higgs bundles over a closed Riemann surface X and their relationship to representations of the fundamental group of X. We construct an equivalence between the deformation theories of flat…

Assuming the extrinsic $Q$-curvature admits a decomposition into the Pfaffian, a scalar conformal submanifold invariant, and a tangential divergence, we prove that the renormalized area of an even-dimensional minimal submanifold of a…

We develop a general theory for irreducible homogeneous spaces $M= G/H$, in relation to the nullity $\nu$ of their curvature tensor. We construct natural invariant (different and increasing) distributions associated with the nullity, that…

After a historical discussion of classical uniformisation results for Riemann surfaces, of problems appearing in higher dimensions, and of uniformisation results for projective manifolds with trivial or ample canonical bundle, we introduce…

In this paper we consider twice-dimensionally reduced, generalized Seiberg-Witten equations, defined on a compact Riemann surface. A novel feature of the reduction technique is that the resulting equations produce an extra "Higgs field".…

We characterize general pseudo-harmonic morphisms from a Riemannian manifold to a Hermitian manifold as pseudo horizontally weakly conformal maps with an additional property. We study to what extent we can (locally) describe these…

In this paper we consider an inverse problem of determining a minimal surface embedded in a Riemannian manifold. We show under a topological condition that if $\Sigma$ is a $2$-dimensional embedded minimal surface, then the knowledge of the…

This paper has studied the three-dimensional Dunkl oscillator models in a generalization of superintegrable Euclidean Hamiltonian systems to curved ones. These models are defined based on curved Hamiltonians, which depend on a deformation…

We extend equivariant dimensional reduction techniques to the case of quantum spaces which are the product of a Kaehler manifold M with the quantum two-sphere. We work out the reduction of bundles which are equivariant under the natural…

One of the unexplored benefits of studying layer potentials on smooth, closed hypersurfaces of Euclidean space is the factorization of the Neumann-Poincar\'e operator into a product of two self-adjoint transforms. Resurrecting some…

Consider a bundle of circles passing through 0 in 4-dimensional space. It is said to be rectifiable if there is a germ of diffeomorphism at 0 that takes all circles from our bundle to straight lines. We will give a classification of all…

A framework allowing for perturbative calculations to be carried out for quantum field theories with arbitrary smoothly curved boundaries is described. It is based on an expansion of the heat kernel derived earlier for arbitrary mixed…

The general construction of self-adjoint configuration space representations of the Heisenberg algebra over an arbitrary manifold is considered. All such inequivalent representations are parametrised in terms of the topology classes of flat…

We present examples of metric spaces that are not Riemannian manifolds nor dimensionally homogeneous that satisfy the Tetrahedral Property. In spite of that, Euclidean cones over metric spaces with small diameter do not satisfy this…

For a class of two-dimensional Euclidean lattice field theories admitting topological lines encoded into a spherical fusion category, we explore aspects of their realisations as boundary theories of a three-dimensional topological quantum…

We propose a geometric object slightly subtler than a complex line bundle with connection, a two-sphere fibration with structure group $\Omega^2_e S^2$, to parametrize a space of dimensional regularizations in the metaphysics of…