Lifting covering maps

Characterization of covering maps via path-lifting property

A continuous map between topological f : X → Y is said to satisfy the path-lifting property if for any path p : [0, 1] → Y and any x ∈ f(p(0)) there exists a lifting p̃ of the path p with the intitial value x, i.e. there exists a path p̃ such that f ◦ p̃ = p and p̃(0) = x. Similarly, a smooth map between Riemannian manifolds f : X → Y is said to satisfy the rectifiable path-lifting property if the ...

Simplicial ramified covering maps

In this paper we define the concept of a ramified covering map in the category of simplicial sets and we show that it has properties analogous to those of the topological ramified covering maps. We show that the geometric realization of a simplicial ramified covering map is a topological ramified covering map, and we also consider the relation with ramified covering maps in the category of simp...

Universal covering Maps and radial

Lifting default for S1-valued maps

Let ' 2 C1([0, 1]N ,R). When 0 < s < 1, p 1 and 1  sp < N , the W s,p-semi-norm |'|W s,p of ' is not controlled by |g|W s,p , where g := eı' [3]. [This question is related to existence, for S1-valued maps g, of a lifting ' as smooth as allowed by g.] In [4], the authors suggested that |g|W s,p does control a weaker quantity, namely |'|W s,p+W 1,sp . Existence of such control is due to J. Bourg...

Lifting GIS Maps into Strong Geometric Context

Contextual information can have a substantial impact on the performance of visual tasks such as semantic segmentation, object detection, and geometric estimation. Data stored in Geographic Information Systems (GIS) offers a rich source of contextual information that has been largely untapped by computer vision. We propose to leverage such information for scene understanding by combining GIS res...