Related papers: Circle Decompositions of Surfaces
We introduce multi-split continuous functions between topological spaces, a weaker form of continuity that generalizes split continuity while being stable under compositions. We will define the associated star multifunction and…
We define a complex connection on a real hypersurface of $\C^{n+1}$ which is naturally inherited from the ambient space. Using a system of Codazzi-type equations, we classify connected real hypersurfaces in $\C^{n+1}$, $n\ge 2$, which are…
We prove that every closed orientable surface S of negative Euler characteristic admits a pair of finite-degree covers which are length isospectral over S but generically not simple length isospectral over S. To do this, we first…
We give examples of open 3-manifolds and 3-orbifolds that exhibit pathological behavior with respect to splitting along surfaces (2-suborbifolds) with nonnegative Euler characteristic.
We describe the topology of singular real algebraic curves in a smooth surface. We enumerate and bound in terms of the degree the number of topological types of singular algebraic curves in the real projective plane.
We exhibit many examples of closed complex surfaces whose diffeomorphism groups are not simply-connected and contain loops that are not homotopic to loops of symplectomorphisms.
We estimate from below the number of lines meeting each of given 4 disjoint smooth closed curves in a given cyclic order in the real projective 3-space and in a given linear order in the Euclidean 3-space. Similarly, we estimate the number…
We classify surface Houghton groups, as well as their pure subgroups, up to isomorphism, commensurability, and quasi-isometry.
A one parameter set of noncommutative complex algebras is given. These may be considered deformation quantisation algebras. The commutative limit of these algebras correspond to the algebra of polynomial functions over a manifold or…
We construct algorithms and topological invariants that allow us to distinguish the topological type of a surface, as well as functions and vector fields for their topological equivalence. In the first part (arXiv:2501.15657), we discused…
We construct algorithms and topological invariants that allow us to distinguish the topological type of a surface, as well as functions and vector fields for their topological equivalence. In the first part we discus the main structures…
A correspondence between different $Pin$-type structures on a compact surface and quadratic (linear) forms on its homology is constructed. Addition of structures is defined and expressed in terms of these quadratic forms.
We study symplectic deformation types of minimal symplectic fillings of links of quotient surface singularities. In particular, there are only finitely many symplectic deformation types for each quotient surface singularity.
Those maps of a closed surface to the three-dimensional torus that are homotopic to embeddings are characterized. Particular attention is paid to the somewhat intricate case when the surface is nonorientable.
Superconformal surfaces in Euclidean space are the ones for which the ellipse of curvature at any point is a nondegenerate circle. They can be characterized as the surfaces for which a well-known pointwise inequality relating the intrinsic…
A set of control points can determine a Bezier surface and a triangulated surface simultaneously. We prove that the triangulated surface becomes homeomorphic and ambient isotopic to the Bezier surface via subdivision. We also show that the…
This expository survey describes how holomorphic quadratic differentials arise in several aspects of Teichm\"uller theory, highlighting their relation with various geometric structures on surfaces. The final section summarizes results for…
We give a new lower bound on the number of connected components of the space of representations of a surface group into the group of orientation preserving homeomorphisms of the circle. Precisely, for the fundamental group of a genus g…
Let $\Gamma_g$ be the fundamental group of a closed connected orientable surface of genus $g\geq2$. We introduce a combinatorial structure of "core surfaces", that represent subgroups of $\Gamma_g$. These structures are (usually)…
In this paper we define $q$-spherical surfaces as the surfaces that contain the absolute conic of the Euclidean space as a $q-$fold curve. Particular attention is paid to the surfaces with singular points of the highest order. Two classes…