Banchoff’s sphere and branched covers over the trefoil
نویسندگان
چکیده
منابع مشابه
Branched Covers of the Riemann Sphere
A (real) manifold of dimension n is a (Hausdorff, second countable) space which is locally homeomorphic to an open subset of Rn. If we wish to make a definition of a complex manifold, we could replace Rn by Cn, but then we see that we have simply given the definition of an even-dimensional real manifold. As with real differentiable manifolds, the key is to add some additional structure via a we...
متن کاملDiscrete uniformization of finite branched covers over the Riemann sphere via hyper-ideal circle patterns
With the help of hyper-ideal circle pattern theory, we have developed a discrete version of the classical uniformization theorems for surfaces represented as finite branched covers over the Riemann sphere as well as compact polyhedral surfaces with non-positive curvature. We show that in the case of such surfaces discrete uniformization via hyper-ideal circle patterns always exists and is uniqu...
متن کاملHyperbolic Structures on Branched Covers over Hyperbolic Links
Using a result of Tian concerning deformation of negatively curved metrics to Einstein metrics, we conclude that, for any fixed link with hyperbolic complement, there is a class of irregular branched covering spaces, branched over that link, effectively detectable by their branching indices, which consists entirely of closed hyperbolic manifolds. Section 0 Introduction. One of the elusive compo...
متن کاملGeometric Structures on Branched Covers over Universal Links
A number of recent results are presented which bear on the question of what geometric information can be gleaned from the representation of a three-manifold as a branched cover over a fixed universal link. Results about Seifert-fibered manifolds, graph manifolds and hyperbolic manifolds are discussed. Section 0 Introduction. Closed, orientable three-manifolds admit a variety of universal constr...
متن کاملConstructing Simplicial Branched Covers
Izmestiev and Joswig described how to obtain a simplicial covering space (the partial unfolding) of a given simplicial complex, thus obtaining a simplicial branched cover [Adv. Geom. 3(2):191-255, 2003]. We present a large class of branched covers which can be constructed via the partial unfolding. In particular, for d ≤ 4 every closed oriented PL d-manifold is the partial unfolding of some pol...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas
سال: 2017
ISSN: 1578-7303,1579-1505
DOI: 10.1007/s13398-017-0477-5