Embedded incompressible surfaces and homology of ramified coverings of three-manifolds

2000 ◽  
Vol 6 (1) ◽  
pp. 1-39 ◽  
Author(s):  
A. Reznikov
Keyword(s):  
Incompressible Surfaces ◽  
Ramified Coverings

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.

Incompressible surfaces in 2-bridge knot complements

1985 ◽  
Vol 79 (2) ◽  
pp. 225-246 ◽  
Author(s):  
A. Hatcher ◽  
W. Thurston
Keyword(s):  
Incompressible Surfaces ◽  
Knot Complements

scholarly journals Least area incompressible surfaces in 3-manifolds

1983 ◽  
Vol 71 (3) ◽  
pp. 609-642 ◽  
Author(s):  
Michael Freedman ◽  
Joel Hass ◽  
Peter Scott
Keyword(s):  
Incompressible Surfaces ◽  
Least Area

Weierstrass multiple points on algebraic curves and ramified coverings

1998 ◽  
Vol 104 (1) ◽  
pp. 335-348 ◽  
Author(s):  
Edoardo Ballico ◽  
Changho Keem
Keyword(s):  
Algebraic Curves ◽  
Multiple Points ◽  
Ramified Coverings

scholarly journals Decomposing Heegaard splittings along separating incompressible surfaces in 3-manifolds

2019 ◽  
Vol 264 ◽  
pp. 21-26
Author(s):  
Kazuhiro Ichihara ◽  
Makoto Ozawa ◽  
J. Hyam Rubinstein
Keyword(s):  
Heegaard Splittings ◽  
Incompressible Surfaces

scholarly journals Closed incompressible surfaces in knot complements

1999 ◽  
Vol 352 (2) ◽  
pp. 655-677 ◽  
Author(s):  
Elizabeth Finkelstein ◽  
Yoav Moriah
Keyword(s):  
Incompressible Surfaces ◽  
Knot Complements
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