ﻻ يوجد ملخص باللغة العربية
We will prove the relative homotopy principle for smooth maps with singularities of a given {cal K}-invariant class with a mild condition. We next study a filtration of the group of homotopy self-equivalences of a given manifold P by considering singularities of non-negative {cal K}-codimensions.
Let $M$ be a smooth manifold and let $F$ be a codimension one, $C^infty$ foliation on $M$, with isolated singularities of Morse type. The study and classification of pairs $(M,F)$ is a challenging (and difficult) problem. In this setting, a classical
We construct a quasiconformally homogeneous hyperbolic Riemann surface-other than the hyperbolic plane-that does not admit a bounded pants decomposition. Also, given a connected orientable topological surface of infinite type with compact boundary co
The local invariants of a meromorphic Abelian differential on a Riemann surface of genus $g$ are the orders of zeros and poles, and the residues at the poles. The main result of this paper is that with few exceptions, every pattern of orders and resi
Let $W$ be a compact smooth $4$-manifold that deformation retract to a PL embedded closed surface. One can arrange the embedding to have at most one non-locally-flat point, and near the point the topology of the embedding is encoded in the singularit
We give a version in characteristic $p>0$ of Mumfords theorem characterizing a smooth complex germ of surface $(X,x)$ by the triviality of the topological fundamental group of $U=Xsetminus {x}$. This note relies on discussions the authors had durin