Related papers: Non-existence of orthogonal complex structures on …

We have identified some necessary conditions for the existence of rigid sphere designs. In particular, we have successfully resolved the conjecture proposed by [Ban87]; Given fixed positive integers t and d, we show that there exist only…

We show that the arc complex $\mathcal{A}(S_{g,1})$ is not quasi-isometric to the sphere complex $\mathcal S_{2g}$ associated to the double of a genus $2g$ handlebody. Along the way, we present a simple proof that $\mathcal{A}(S_{g,1})$ is…

In this paper, we develop spectral analysis of a discrete non-Hermitian quantum system that is a discrete counterpart of some continuous quantum systems on a complex contour. In particular, simple conditions for discreteness of the spectrum…

We construct several rigid (i.e., unique in their deformation class) surfaces which have particular behavior with respect to real structures: in one example the surface has no any real structure, in the other one it has a unique real…

Complex dynamical systems on the Riemann sphere do not possess ``invariant forms''. However there exist non-trivial examples of dynamical systems, defined over number fields, satisfying the property that their reduction modulo $\wp$…

We prove that there is no consistent polynomial quantization of the coordinate ring of a basic non-nilpotent coadjoint orbit of a semisimple Lie group.

We compute small rational models for configuration spaces of points on oriented surfaces, as right modules over the framed little disks operad. We do this by splitting these surfaces in unions of several handles. We first describe rational…

We construct the first examples of non-K\"ahler complex structures on $R^4$. These complex surfaces have some analogies with the complex structures constructed in early Fifties by Calabi and Eckmann on the products of two odd-dimensional…

We describe a construction of Riemannian metrics of nonnegative sectional curvature on a closed smooth nonorientable 4-manifold with fundamental group of order two that realizes a homotopy class that was not previously known to contain…

We observed in our previous paper that all the complex structures on four-dimensional compact solvmanifolds, including tori, are left-invariant. In this paper we will give an example of a six-dimensional compact solvmanifold which admits a…

This paper contains detailed proofs of our results on the moduli space and the structure of noncommutative 3-spheres. We develop the notion of central quadratic form for quadratic algebras, and a general theory which creates a bridge…

We prove that there does not exist any connected topological proper loop homeomorphic to a quasi-simple Lie group and having a compact Lie group as the group topologically generated by its left translations. Moreover, any connected…

Finding necessary conditions for the geometry of flexible polyhedra is a classical problem that has received attention also in recent times. For flexible polyhedra with triangular faces, we showed in a previous work the existence of cycles…

In this short note we update a result proved in [16]. This will complete our program of [12] showing that the structure set vanishes for compact aspherical 3-manifolds.

We classify non-nilpotent complex structures on 6-nilmanifolds and their associated invariant balanced metrics. As an application we find a large family of solutions of the heterotic supersymmetry equations with non-zero flux, non-flat…

Approximate symmetries of geodesic equations on 2-spheres are studied. These are the symmetries of the perturbed geodesic equations which represent approximate path of a particle rather than exact path. After giving the exact symmetries of…

We construct two-dimensional families of complex hyperbolic structures on disc orbibundles over the sphere with three cone points. This contrasts with the previously known examples of the same type, which are locally rigid. In particular,…

We show that there are no nontrivial solutions of the Seiberg-Witten equations on R^8 with constant standard spin^c structure.

We give a structural theorem for pseudofinite groups of finite centraliser dimension. As a corollary, we observe that there is no finitely generated pseudofinite group of finite centraliser dimension.

For each nonnegative integer m we show that any closed, oriented topological four-manifold with fundamental group Z_{4m+2} and odd intersection form, with possibly seven exceptions, either admits no smooth structure or admits infinitely…