On regular homotopy of branched coverings of the sphere

1977 ◽  
Vol 21 (3) ◽  
pp. 293-306 ◽  
Author(s):  
Ulrich Hirsch
Keyword(s):  
Branched Coverings ◽  
Regular Homotopy

scholarly journals Harmonic branched coverings and uniformization of CAT(k) spheres

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Christine Breiner ◽  
Chikako Mese
Keyword(s):  
Harmonic Map ◽  
Branched Coverings ◽  
Curvature Bound ◽  
Branched Covering

Abstract Let S be a surface with a metric d satisfying an upper curvature bound in the sense of Alexandrov (i.e. via triangle comparison). We show that an almost conformal harmonic map from a surface into ( S , d ) {(S,d)} is a branched covering. As a consequence, if ( S , d ) {(S,d)} is homeomorphically equivalent to the 2-sphere 𝕊 2 {\mathbb{S}^{2}} , then it is conformally equivalent to 𝕊 2 {\mathbb{S}^{2}} .

Branched Coverings and Minimal Free Resolution for Infinite-Dimensional Complex Spaces

2003 ◽  
Vol 10 (1) ◽  
pp. 37-43
Author(s):  
E. Ballico
Keyword(s):  
Projective Space ◽  
Projective Spaces ◽  
Free Resolution ◽  
Complete Intersections ◽  
Vanishing Theorem ◽  
Sheaf Cohomology ◽  
Minimal Free Resolution ◽  
Branched Coverings ◽  
Infinite Dimensional ◽  
Complex Spaces

Abstract We consider the vanishing problem for higher cohomology groups on certain infinite-dimensional complex spaces: good branched coverings of suitable projective spaces and subvarieties with a finite free resolution in a projective space P(V ) (e.g. complete intersections or cones over finitedimensional projective spaces). In the former case we obtain the vanishing result for H 1. In the latter case the corresponding results are only conditional for sheaf cohomology because we do not have the corresponding vanishing theorem for P(V ).

scholarly journals CycIic branched coverings of 2-bridgeknots

1999 ◽  
Vol 12 (2) ◽  
Author(s):  
Beatrice Ruini ◽  
Fulvia Spaggiari ◽  
Alberto Cavicchioli
Keyword(s):  
Branched Coverings

Dehn surgeries on some classical links

2011 ◽  
Vol 54 (1) ◽  
pp. 33-45 ◽  
Author(s):  
Alberto Cavicchioli ◽  
Fulvia Spaggiari ◽  
Agnese Ilaria Telloni
Keyword(s):  
Dehn Surgery ◽  
Fundamental Groups ◽  
Branched Coverings ◽  
Borromean Rings

AbstractWe consider orientable closed connected 3-manifolds obtained by performing Dehn surgery on the components of some classical links such as Borromean rings and twisted Whitehead links. We find geometric presentations of their fundamental groups and describe many of them as 2-fold branched coverings of the 3-sphere. Finally, we obtain some topological applications on the manifolds given by exceptional surgeries on hyperbolic 2-bridge knots.

scholarly journals Lifting of homeomorphisms to 4-sheeted branched coverings of a disk

2008 ◽  
Vol 155 (16) ◽  
pp. 1820-1839
Author(s):  
Bronislaw Wajnryb ◽  
Agnieszka Wisniowska-Wajnryb
Keyword(s):  
Branched Coverings

Immersions with non-zero normal vector fields

1992 ◽  
Vol 112 (2) ◽  
pp. 281-285 ◽  
Author(s):  
Bang-He Li ◽  
Gui-Song Li
Keyword(s):  
Vector Fields ◽  
Normal Vector ◽  
Homotopy Classes ◽  
Natural Action ◽  
Singularity Method ◽  
One To One ◽  
Regular Homotopy

Let M be a smooth n-manifold, X be a smooth (2n − 1)-manifold, and g:M → X be a map. It was proved in [6] that g is always homotopic to an immersion. The set of homotopy classes of monomorphisms from TM into g*TX, which is denoted by Sg, may be enumerated either by the method of I. M. James and E. Thomas or by the singularity method of U. Koschorke (see [1] and references therein). When the natural action of π1(XM, g) on Sg is trivial, for example, if X is euclidean, the set Sg is in one-to-one correspondence with the set of regular homotopy classes of immersions homotopic to g (see e.g. [4]).

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