Related papers: Arithmetic modular links
Enumerative algebraic geometry counts the solutions to certain geometric constraints. Numerical algebraic geometry determines these solutions for any given instance. This article illustrates how these two fields complement each other. Our…
We classify the $3$-manifolds obtained as the preimages of arcs on the plane for simplified $(2, 0)$-trisection maps, which we call vertical $3$-manifolds. Such a $3$-manifold is a connected sum of a $6$-tuple of vertical $3$-manifolds over…
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 extend calculus from smooth manifolds to topological manifolds making use of a theory of generalized functions developed for this aim. Actually such extension fits into a boarder context: the universal construction of a site containing…
Starting from a divide, i.e. a generic immersion of finitely many copies of the interval [0,1] in the disk, we construct a classical link in the 3-sphere. We prove that the link's complement fibers over the circle, if the divide is…
The intersection matrix of a simplicial complex has entries equal to the rank of the intersection of its facets. In [1] the authors prove the intersection matrix is enough to determine a triangulation of a surface up to isomorphism. In this…
The linear transports along paths in vector bundles introduced in Ref. [1] are applied to the special case of tensor bundles over a given differentiable manifold. Links with the transports along paths generated by derivations of tensor…
The goal of this paper is the study of simple rank 2 parabolic vector bundles over a $2$-punctured elliptic curve $C$. We show that the moduli space of these bundles is a non-separated gluing of two charts isomorphic to $\mathbb{P}^1 \times…
Infinitesimal symmetries of $S^1$-bundle gerbes are modelled with multiplicative vector fields on Lie groupoids. It is shown that a connective structure on a bundle gerbe gives rise to a natural horizontal lift of multiplicative vector…
We extend to the context of hyperbolic 3-manifolds with geodesic boundary Thurston's approach to hyperbolization by means of geometric triangulations. In particular, we introduce moduli for (partially) truncated hyperbolic tetrahedra, and…
We introduce and study arithmetic polygons. We show that these arithmetic polygons are connected to triples of square pyramidal numbers. For every odd $N\geq3$, we prove that there is at least one arithmetic polygon with $N$ sides. We also…
This paper describes a way to subdivide a 3-manifold into angled blocks, namely polyhedral pieces that need not be simply connected. When the individual blocks carry dihedral angles that fit together in a consistent fashion, we prove that a…
We construct a small, hyperbolic 3-manifold $M$ such that, for any integer $g\geq 2$, there are infinitely many separating slopes $r$ in $\partial M$ so that $M(r)$, the 3-manifold obtained by attaching a 2-handle to $M$ along $r$, is…
We describe the construction of an $\mathcal{A}_\infty$ multi-module in terms of counts of holomorphic polygons in a series Heegaard multi-diagrams. We show that this is quasi-isomorphic to the type-A bordered-sutured invariant of a link…
We construct a converging geometric iterated function system on the moduli space of ordered triangles, for which the involved functions have geometric meanings and contain a non-contraction map under the natural metric.
We use hypersurfaces containing unexpected linear spaces to construct interesting vector bundles on complete intersection surfaces in projective space. We discover examples of moduli spaces of rank 2 stable bundles on surfaces of Picard…
We describe an explicit open book decomposition adapted to the canonical contact structure on the unit cotangent bundle of a compact surface.
I will discuss results of three different types in geometry and topology. (1) General vanishing and rigidity theorems of elliptic genera proved by using modular forms, Kac-Moody algebras and vertex operator algebras. (2) The computations of…
We study geometric aspects of horizontal 2-plane distributions on the complement of the zero section in the 5-dimensional total space of a rank-3 vector bundle equipped with connection over a surface. We show that any surface in…
The moduli space of jets of certain G-structures (basically those which admit a canonical linear connection) is shown to be isomorphic to the quotient of a natural G-module by G.