Related papers: Horizontality with infinite complexity in the twis…
We establish upper bounds for the complexity of Seifert fibered manifolds with nonempty boundary. In particular, we obtain potentially sharp bounds on the complexity of torus knot complements.
This paper presents a combinatorial analog of topological complexity for finite spaces. We demonstrate that this coincides with the genuine topological complexity of the original finite space, and constitutes an upper bound for the…
We construct a Fourier--Mukai transform for smooth complex vector bundles $E$ over a torus bundle $\pi:M \to B,$ the vector bundles being endowed with various structures of increasing complexity. At a minimum, we consider vector bundles $E$…
We consider a closed odd-dimensional oriented manifold $M$ together with an acyclic flat hermitean vector bundle $\cF$. We form the trivial fibre bundle with fibre $M$ over the manifold of all Riemannian metrics on $M$. It has a natural…
Higgs bundles over a closed orientable surface can be defined for any real reductive Lie group G. In this paper we examine the case G=SO*(2n). We describe a rigidity phenomenon encountered in the case of maximal Toledo invariant. Using this…
Complex supermanifold structures being deformations of the exterior algebra of a holomorphic vector bundle, have been parametrized by orbits of a group on non-abelian cohomology by P. Green. For the case of odd dimension $4$ and $5$ an…
We consider rotations on the torus $\mathbb{T}^2$, and we classify them with respect to the complexity functions. In dimension one, a minimal rotation can be coded by a sturmian word. A sturmian word has complexity $n+1$ by the…
In this paper, we study upper bounds for the topological complexity of the total spaces of some classes of fibre bundles. We calculate a tight upper bound for the topological complexity of an $n$-dimensional Klein bottle. We also compute…
We present a new class of near-horizon geometries which solve Einstein's vacuum equations, including a negative cosmological constant, in all even dimensions greater than four. Spatial sections of the horizon are inhomogeneous S^2-bundles…
We study the geometry of type II supergravity compactifications in terms of an oriented vector bundle $E$, endowed with a bundle metric of split signature and further datum. The geometric structure is associated with a so-called generalised…
A hypercomplex manifold is by definition a smooth manifold equipped with two anticommuting integrable almost complex structures. For example, every hyperkaehler manifold is canonically hypercomplex (the converse is not true). For every…
In four spacetime dimensions, the classically integrable self-dual sectors of gauge theory and gravity have associated chiral algebras, which emerge naturally from their description in twistor space. We show that there are similar chiral…
We study the holomorphic vector bundles E over the twistor space Tw(M) of a compact simply connected hyperk\"ahler manifold $M$. We give a characterization of the semistability condition for E in terms of its restrictions to the holomorphic…
In this paper, we study the nonemptiness, compactness, uniqueness, and finiteness of the solution set of a new type of nonlinear complementarity problem, namely the extended horizontal tensor complementarity problem (EHTCP). We introduce…
We investigate the triangle singularity $f=x^a+y^b+z^c$, or $S=k[x,y,z]/(f)$, attached to a weighted projective line $X$ given by the weight triple $(a,b,c)$. We investigate the stable category of vector bundles on $X$ obtained from the…
This paper attempts to investigate the space of various characteristic classes for smooth manifold bundles with local system on the total space inducing a finite holonomy covering. These classes are known as twisted higher torsion classes.…
Although the interpretation of complexity in extended theories of gravity is available in the literature, its illustration in $f(R,L_{m},\mathcal{T})$ theory is still ambiguous. The orthogonal decomposition of the Riemann tensor results in…
We study a certain type of wild harmonic bundles in relation with a Toda equation. We explain how to obtain a classification of the real valued solutions of the Toda equation in terms of their parabolic weights, from the viewpoint of the…
Heterotic string theory compactified on a K3 surface times T^2 is believed to be equivalent to type II string theory on a suitable Calabi-Yau threefold. In particular, it must share the same hypermultiplet moduli space. Building on the…
We introduce integrable complex structures on twistor spaces fibered over complex manifolds. We then show, in particular, that the twistor spaces associated with generalized Kahler, SKT and strong HKT manifolds all naturally admit complex…