ON THE H-REGULAR COVERING MAP AT A POINT

2020 ◽  
Vol 25 (1-2) ◽  
pp. 1-9
Author(s):  
Majid Kowkabi ◽  
Hamid Torabi
Keyword(s):  
Regular Covering ◽  
Covering Map

scholarly journals Equivalent conditions for digital covering maps

Filomat ◽  
2020 ◽  
Vol 34 (12) ◽  
pp. 4005-4014
Author(s):  
Ali Pakdaman ◽  
Mehdi Zakki
Keyword(s):  
Local Isomorphism ◽  
Covering Map ◽  
Unique Path ◽  
Continuous Surjection ◽  
Digital Covering ◽  
Equivalent Conditions ◽  
Digital Spaces

It is known that every digital covering map p:(E,k) ? (B,?) has the unique path lifting property. In this paper, we show that its inverse is true when the continuous surjective map p has no conciliator point. Also, we prove that a digital (k,?)-continuous surjection p:(E,k)? (B,?) is a digital covering map if and only if it is a local isomorphism, when all digital spaces are connected. Moreover, we find out a loop criterion for a digital covering map to be a radius n covering map.

scholarly journals Regular covering surfaces of Riemann surfaces

1960 ◽  
Vol 10 (4) ◽  
pp. 1263-1289
Author(s):  
Sidney Harmon
Keyword(s):  
Riemann Surfaces ◽  
Regular Covering

Arc-transitive abelian regular covering graphs

2016 ◽  
Vol 26 (07) ◽  
pp. 1369-1393 ◽  
Author(s):  
Jicheng Ma
Keyword(s):  
Complete Graph ◽  
Abelian Groups ◽  
Cubic Graphs ◽  
New Approach ◽  
Regular Covering ◽  
Symmetric Graphs

A lot of attention has been paid recently to the construction of symmetric covers of symmetric graphs. After a new approach given by Conder and the author [Arc-transitive abelian regular covers of cubic graphs, J. Algebra 387 (2013) 215–242], the group of covering transformations can be extended to more general abelian groups rather than cyclic or elementary abelian groups. In this paper, by using the Conder–Ma approach, we investigate the symmetric covers of 4-valent symmetric graphs. As an application, all the arc-transitive abelian regular covers of the 4-valent complete graph [Formula: see text] which can be obtained by lifting the arc-transitive subgroups of automorphisms [Formula: see text] and [Formula: see text] are classified.

scholarly journals Arc-Transitive Dihedral Regular Covers of Cubic Graphs

10.37236/4035 ◽  
2014 ◽  
Vol 21 (3) ◽  
Author(s):  
Jicheng Ma
Keyword(s):  
Transformation Group ◽  
Petersen Graph ◽  
Cubic Graphs ◽  
Regular Covering ◽  
Symmetric Graphs ◽  
Cyclic Covers ◽  
Covering Projection

A regular covering projection is called dihedral or abelian if the covering transformation group is dihedral or abelian. A lot of work has been done with regard to the classification of arc-transitive abelian (or elementary abelian, or cyclic) covers of symmetric graphs. In this paper, we investigate arc-transitive dihedral regular covers of symmetric (arc-transitive) cubic graphs. In particular, we classify all arc-transitive dihedral regular covers of $K_4$, $K_{3,3}$, the 3-cube $Q_3$ and the Petersen graph.

scholarly journals Weighted Zeta Functions of Graph Coverings

10.37236/1117 ◽  
2006 ◽  
Vol 13 (1) ◽  
Author(s):  
Iwao Sato
Keyword(s):  
Zeta Function ◽  
Zeta Functions ◽  
Equivalence Classes ◽  
Signed Graphs ◽  
Base Graph ◽  
Regular Covering ◽  
Decomposition Formula ◽  
Graph Coverings

We present a decomposition formula for the weighted zeta function of an irregular covering of a graph by its weighted $L$-functions. Moreover, we give a factorization of the weighted zeta function of an (irregular or regular) covering of a graph by equivalence classes of prime, reduced cycles of the base graph. As an application, we discuss the structure of balanced coverings of signed graphs.

scholarly journals Compactifying sufficiently regular covering spaces of compact 3-manifolds

2000 ◽  
Vol 128 (5) ◽  
pp. 1507-1513 ◽  
Author(s):  
Robert Myers
Keyword(s):  
Covering Spaces ◽  
Regular Covering

scholarly journals An explicit relation between knot groups in lens spaces and those in S3

2018 ◽  
Vol 27 (08) ◽  
pp. 1850045
Author(s):  
Yuta Nozaki
Keyword(s):  
Fundamental Group ◽  
Lens Space ◽  
Lens Spaces ◽  
Alternative Proof ◽  
Cyclic Covering ◽  
Covering Map ◽  
Explicit Relation

For a cyclic covering map [Formula: see text] between two pairs of a 3-manifold and a knot each, we describe the fundamental group [Formula: see text] in terms of [Formula: see text]. As a consequence, we give an alternative proof for the fact that certain knots in [Formula: see text] cannot be represented as the preimage of any knot in a lens space, which is related to free periods of knots. In our proofs, the subgroup of a group [Formula: see text] generated by the commutators and the [Formula: see text]th power of each element of [Formula: see text] plays a key role.

scholarly journals Stackings and the W-cycles Conjecture

2017 ◽  
Vol 60 (3) ◽  
pp. 604-612 ◽  
Author(s):  
Larsen Louder ◽  
Henry Wilton
Keyword(s):  
Euler Characteristic ◽  
Schur Multiplier ◽  
Finitely Generated ◽  
Covering Map ◽  
Compact Graph

AbstractWe prove Wise’s W-cycles conjecture. Consider a compact graph Γ' immersing into another graph Γ. For any immersed cycle Λ: S1 ⟶ Γ, we consider the map Λ' from the circular components 𝕊 of the pullback to Γ'. Unless Λ' is reducible, the degree of the covering map 𝕊 ⟶ S1 is bounded above by minus the Euler characteristic of Γ'. As a corollary, any finitely generated subgroup of a one-relator group has a finitely generated Schur multiplier.

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