scholarly journals Simplicial ramified covering maps

2008 ◽  
Vol 156 (2) ◽  
pp. 205-216 ◽  
Author(s):  
Marcelo A. Aguilar ◽  
Carlos Prieto
Keyword(s):  
Ramified Covering

scholarly journals Convergence of Discrete Period Matrices and Discrete Holomorphic Integrals for Ramified Coverings of the Riemann Sphere

2021 ◽  
Vol 24 (3) ◽  
Author(s):  
Alexander I. Bobenko ◽  
Ulrike Bücking
Keyword(s):  
Error Estimate ◽  
Branch Point ◽  
Riemann Surfaces ◽  
Riemann Sphere ◽  
Holomorphic Functions ◽  
Convergence Result ◽  
Edge Length ◽  
Ramified Covering ◽  
Compact Riemann Surfaces ◽  
Ramified Coverings

AbstractWe consider the class of compact Riemann surfaces which are ramified coverings of the Riemann sphere $\hat {\mathbb {C}}$ ℂ ̂ . Based on a triangulation of this covering we define discrete (multivalued) harmonic and holomorphic functions. We prove that the corresponding discrete period matrices converge to their continuous counterparts. In order to achieve an error estimate, which is linear in the maximal edge length of the triangles, we suitably adapt the triangulations in a neighborhood of every branch point. Finally, we also prove a convergence result for discrete holomorphic integrals for our adapted triangulations of the ramified covering.

scholarly journals The Number of Ramified Covering of a Riemann Surface by Riemann Surface

2000 ◽  
Vol 213 (3) ◽  
pp. 685-696 ◽  
Author(s):  
An-Min Li ◽  
Guosong Zhao ◽  
Quan Zheng
Keyword(s):  
Riemann Surface ◽  
Ramified Covering

scholarly journals Transfers for ramified covering maps in homology and cohomology

2006 ◽  
Vol 2006 ◽  
pp. 1-28 ◽  
Author(s):  
Marcelo A. Aguilar ◽  
Carlos Prieto
Keyword(s):  
Topological Groups ◽  
Ramified Covering ◽  
The One ◽  
Definition Of

Making use of a modified version, due to McCord, of the Dold-Thom construction of ordinary homology, we give a simple topological definition of a transfer for ramified covering maps in homology with arbitrary coefficients. The transfer is induced by a suitable map between topological groups. We also define a new cohomology transfer which is dual to the homology transfer. This duality allows us to show that our homology transfer coincides with the one given by L. Smith. With our definition of the homology transfer we can give simpler proofs of the properties of the known transfer and of some new ones. Our transfers can also be defined in Karoubi's approach to homology and cohomology. Furthermore, we show that one can define mixed transfers from other homology or cohomology theories to the ordinary ones.

On the homology of a ramified covering over ℂ2

1998 ◽  
Vol 64 (6) ◽  
pp. 726-731 ◽  
Author(s):  
A. G. Vitushkin
Keyword(s):  
Ramified Covering

Transfer and ramified coverings

1983 ◽  
Vol 93 (3) ◽  
pp. 485-493 ◽  
Author(s):  
Larry Smith
Keyword(s):  
Finite Group ◽  
Orbit Space ◽  
Covering Spaces ◽  
Branched Covering ◽  
Ramified Covering ◽  
Arbitrary Finite Group ◽  
Transfer Homomorphism ◽  
Image Position ◽  
A Finite Group ◽  
Ramified Coverings

AbstractIn this note we introduce a general class of finite ramified coverings π X˜ ↓ X. Examples of ramified covers in our sense include: finite covering spaces, branched covering spaces and the orbit map Y ↓ Y/G where G is a finite group and Y an arbitrary G-space. For any d-fold ramified covering π: X˜ ↓ X we construct a transfer homomorphismwith the expected property thatis multiplication by d. As a consequence we obtain a simple proof of the Conner conjecture; viz. the orbit space of an arbitrary finite group action on a ℚ-acyclic space is again ℚ acyclic.

scholarly journals A classification of cohomology transfers for ramified covering maps

2006 ◽  
Vol 189 (1) ◽  
pp. 1-25 ◽  
Author(s):  
Marcelo A. Aguilar ◽  
Carlos Prieto
Keyword(s):  
Ramified Covering

scholarly journals The transfer for ramified covering G-maps

2010 ◽  
Vol 22 (6) ◽  
Author(s):  
Marcelo A. Aguilar ◽  
Carlos Prieto
Keyword(s):  
Ramified Covering

CURRENT-CURRENT CORRELATION FUNCTION ON ALGEBRAIC CURVES

1993 ◽  
Vol 08 (12) ◽  
pp. 1153-1159 ◽  
Author(s):  
JAN SOBCZYK
Keyword(s):  
Correlation Function ◽  
Riemann Surface ◽  
Algebraic Curves ◽  
Energy Momentum Tensor ◽  
Momentum Tensor ◽  
Expectation Value ◽  
Current Correlation Function ◽  
Current Correlation ◽  
Ramified Covering ◽  
A Current

We derive an explicit expression for a current-current correlation function on a Riemann surface represented as 3 sheets ramified covering over CP(1). The method used in the paper can be easily applied to more general algebraic curves. Knowledge of G(z, w) enables calculation of the expectation value of the energy momentum tensor for scalar field.

Ramified coverings, orbit projections and symmetric powers

1986 ◽  
Vol 99 (1) ◽  
pp. 65-72 ◽  
Author(s):  
Albrecht Dold
Keyword(s):  
Finite Group ◽  
Symmetric Powers ◽  
Ramified Covering ◽  
A Finite Group ◽  
Ramified Coverings

L. Smith, in a recent paper [11], studied a class of maps X →Y which he called ramified coverings. Roughly speaking, these are maps with a multiple-valued inverse Y → SPdX; cf. 1·1. He showed that X → X/G is a ramified covering whenever a finite group G acts on X. Using results of [4] on infinite symmetric powers SP∞X of CW-complexes X he obtained transfer homomorphisms .

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