Related papers: Note on the structure constants for the diffeomorp…
We identify the space of left-invariant oriented complex structures on the complex Heisenberg group, and prove that it has the homotopy type of the disjoint union of a point and a 2-sphere.
In this note we obtain a formula for the sectional curvature on an arbitrary two-dimensional smooth manifold $M$ equipped with a Lorentzian metric $g$.
The Fourier transform of the indicator function of arbitrary polygons and polyhedra is computed for complex wavevectors. Using the divergence theorem and Stokes' theorem, closed expressions are obtained. Apparent singularities, all…
This is the first of two papers establishing structural properties of ${\cal R}_2$.
We derive simplified normal forms for an area-preserving map in a neighbourhood of a degenerate resonant elliptic fixed point. Such fixed points appear in generic two-parameter families of area-preserving maps. We also derive a simplified…
There are a least uncountably many diffeomorphism types for open manifolds. Hence the classification problem is extremely difficult. We proceed as follows: We define several uniform structures of proper metric spaces and consider their arc…
We give a complete characterization of those essential simple loops on 2-bridge spheres of 2-bridge links which are null-homotopic in the link complements. By using this result, we describe all upper-meridian-pair-preserving epimorphisms…
In this paper we construct two groupoids from morphisms of groupoids, with one from a categorical viewpoint and the other from a geometric viewpoint. We show that for each pair of groupoids, the two kinds of groupoids of morphisms are…
We establish a connection between Morin singularities and stable homotopy groups of spheres. This connection allows us to describe how the images of singularity strata behave around the image of a more complicated stratum.
An isoparametric family in the unit sphere consists of parallel isoparametric hypersurfaces and their two focal submanifolds. The present paper has two parts. The first part investigates topology of the isoparametric families, namely the…
The class of self-similar 2-manifolds consists of manifolds exhibiting a type of homogeneity akin to the 2-sphere and the Cantor set, and includes both the 2-sphere and the 2-sphere with a Cantor set removed. This chapter aims to provide a…
We consider the problem of defining the structure of a smooth manifold on the various spaces of piecewise-smooth loops in a smooth finite dimensional manifold. We succeed for a particular type of piecewise-smooth loops. We also examine the…
This article is a continuation of work on construction and calculation various of modifications of invariant based on the use Euclidean metric values attributed to elements of manifold triangulation. We again address the well investigated…
Let $\Diffeo=\Diffeo(\R)$ denote the group of infinitely-differentiable diffeomorphisms of the real line $\R$, under the operation of composition, and let $\Diffeo^+$ be the subgroup of diffeomorphisms of degree +1, i.e.…
In this paper we study three-dimensional orbifolds by 2-groups with a trivially-acting one-form symmetry group BK. These orbifolds have a global two-form symmetry, and so one expects that they decompose into (are equivalent to) a disjoint…
We find some explicit bounds on the ${\mathcal L}(L^2)$-norm of pseudo-differential operators with symbols defined by a metric on the phase space. In particular, we prove that this norm depends only on the "structure constants" of the…
Phase equations describing the evolution of large scale modulation of spatially periodic patterns in two dimensional systems are derived by employing the renormalization group method. A general formula for phase diffusion coefficients is…
In this short exposition we provide a simplified proof of Buser's result for Cheeger's isoperimetric constant.
We study the dynamics of generic unfoldings of saddle-node circle local diffeomorphisms from the measure theoretical point of view, obtaining statistical stability results for deterministic and random perturbations in these kind of…
We illuminate the relation between the Bruhat order on the symmetric group and structure constants (Littlewood-Richardson coefficients) for the cohomology of the flag manifold in terms of its basis of Schubert classes. Equivalently, the…