FORTRAN Program for the Computation of the First Integral Homology Group of 3-Dimensional Manifolds, Considered as Branched Covering Spaces of the 3-Sphere

1971 ◽  
Vol 25 (115) ◽  
pp. 631
Author(s):  
Robert Riley
Keyword(s):  
Homology Group ◽  
First Integral ◽  
Fortran Program ◽  
Integral Homology ◽  
Covering Spaces ◽  
3 Dimensional ◽  
Branched Covering

Homology Invariants

1978 ◽  
Vol 30 (03) ◽  
pp. 655-670 ◽  
Author(s):  
Richard Hartley ◽  
Kunio Murasugi
Keyword(s):  
Homology Group ◽  
Covering Space ◽  
Simple Relationship ◽  
Cyclic Covering ◽  
Covering Spaces ◽  
Homology Groups ◽  
Branched Covering ◽  
The Relationship

There have been few published results concerning the relationship between the homology groups of branched and unbranched covering spaces of knots, despite the fact that these invariants are such powerful invariants for distinguishing knot types and have long been recognised as such [8]. It is well known that a simple relationship exists between these homology groups for cyclic covering spaces (see Example 3 in § 3), however for more complicated covering spaces, little has previously been known about the homology group, H1(M) of the branched covering space or about H1(U), U being the corresponding unbranched covering space, or about the relationship between these two groups.

Branched Covering Spaces and the Quadratic Forms of Links

1954 ◽  
Vol 59 (3) ◽  
pp. 539 ◽  
Author(s):  
R. H. Kyle
Keyword(s):  
Quadratic Forms ◽  
Covering Spaces ◽  
Branched Covering

Construction and visualization of branched covering spaces

2016 ◽  
Author(s):  
Sanaz Golbabaei ◽  
Lawrence Roy ◽  
Prashant Kumar ◽  
Eugene Zhang
Keyword(s):  
Covering Spaces ◽  
Branched Covering

scholarly journals Existence of Taut Foliations on Seifert Fibered Homology 3-spheres

2014 ◽  
Vol 66 (1) ◽  
pp. 141-169
Author(s):  
Shanti Caillat-Gibert ◽  
Daniel Matignon
Keyword(s):  
Homology Group ◽  
Integral Homology

AbstractThis paper concerns the problem of existence of taut foliations among 3-manifolds. From the work of David Gabai we know that a closed 3-manifold with non-trivial second homology group admits a taut foliation. The essential part of this paper focuses on Seifert fibered homology 3-spheres. The result is quite different if they are integral or rational but non-integral homology 3-spheres. Concerning integral homology 3-spheres, we can see that all but the 3-sphere and the Poincaré 3-sphere admit a taut foliation. Concerning non-integral homology 3-spheres, we prove there are infinitely many that admit a taut foliation, and infinitely many without a taut foliation. Moreover, we show that the geometries do not determine the existence of taut foliations on non-integral Seifert fibered homology 3-spheres.

Strongly-cyclic branched coverings and the Alexander polynomial of knots in rational homology spheres

2007 ◽  
Vol 142 (2) ◽  
pp. 259-268 ◽  
Author(s):  
YUYA KODA
Keyword(s):  
Fundamental Group ◽  
Homology Group ◽  
Alexander Polynomial ◽  
Homology Sphere ◽  
Cyclic Covering ◽  
Rational Homology ◽  
Branched Coverings ◽  
Branched Covering ◽  
Rational Homology Spheres ◽  
Rational Homology Sphere

AbstractLet K be a knot in a rational homology sphere M. In this paper we correlate the Alexander polynomial of K with a g-word cyclic presentation for the fundamental group of the strongly-cyclic covering of M branched over K. We also give a formula for the order of the first homology group of the strongly-cyclic branched covering.

Interactive Design and Visualization of Branched Covering Spaces

2018 ◽  
Vol 24 (1) ◽  
pp. 843-852 ◽  
Author(s):  
Lawrence Roy ◽  
Prashant Kumar ◽  
Sanaz Golbabaei ◽  
Yue Zhang ◽  
Eugene Zhang
Keyword(s):  
Interactive Design ◽  
Covering Spaces ◽  
Branched Covering

scholarly journals Constructions of two-fold branched covering spaces

1986 ◽  
Vol 125 (2) ◽  
pp. 415-446 ◽  
Author(s):  
José Montesinos-Amilibia ◽  
Wilbur Whitten
Keyword(s):  
Covering Spaces ◽  
Branched Covering

scholarly journals Cobordism of branched covering spaces

1980 ◽  
Vol 87 (2) ◽  
pp. 335-345 ◽  
Author(s):  
Hugh Hilden ◽  
Robert D. Little
Keyword(s):  
Covering Spaces ◽  
Branched Covering
Sign in / Sign up

Export Citation Format

Share Document