Ultra regular covering space and its automorphism group

Sang-Eon Han

International Journal of Applied Mathematics and Computer Science (2010)

  • Volume: 20, Issue: 4, page 699-710
  • ISSN: 1641-876X

Abstract

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In order to classify digital spaces in terms of digital-homotopic theoretical tools, a recent paper by Han (2006b) (see also the works of Boxer and Karaca (2008) as well as Han (2007b)) established the notion of regular covering space from the viewpoint of digital covering theory and studied an automorphism group (or Deck's discrete transformation group) of a digital covering. By using these tools, we can calculate digital fundamental groups of some digital spaces and classify digital covering spaces satisfying a radius 2 local isomorphism (Boxer and Karaca, 2008; Han, 2006b; 2008b; 2008d; 2009b). However, for a digital covering which does not satisfy a radius 2 local isomorphism, the study of a digital fundamental group of a digital space and its automorphism group remains open. In order to examine this problem, the present paper establishes the notion of an ultra regular covering space, studies its various properties and calculates an automorphism group of the ultra regular covering space. In particular, the paper develops the notion of compatible adjacency of a digital wedge. By comparing an ultra regular covering space with a regular covering space, we can propose strong merits of the former.

How to cite

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Sang-Eon Han. "Ultra regular covering space and its automorphism group." International Journal of Applied Mathematics and Computer Science 20.4 (2010): 699-710. <http://eudml.org/doc/208019>.

@article{Sang2010,
abstract = {In order to classify digital spaces in terms of digital-homotopic theoretical tools, a recent paper by Han (2006b) (see also the works of Boxer and Karaca (2008) as well as Han (2007b)) established the notion of regular covering space from the viewpoint of digital covering theory and studied an automorphism group (or Deck's discrete transformation group) of a digital covering. By using these tools, we can calculate digital fundamental groups of some digital spaces and classify digital covering spaces satisfying a radius 2 local isomorphism (Boxer and Karaca, 2008; Han, 2006b; 2008b; 2008d; 2009b). However, for a digital covering which does not satisfy a radius 2 local isomorphism, the study of a digital fundamental group of a digital space and its automorphism group remains open. In order to examine this problem, the present paper establishes the notion of an ultra regular covering space, studies its various properties and calculates an automorphism group of the ultra regular covering space. In particular, the paper develops the notion of compatible adjacency of a digital wedge. By comparing an ultra regular covering space with a regular covering space, we can propose strong merits of the former.},
author = {Sang-Eon Han},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {digital image; digital isomorphism; (ultra) regular covering space; digital covering space; simply k-connected; Deck's discrete transformation group; compatible adjacency; digital wedge; automorphism group; simply -connected},
language = {eng},
number = {4},
pages = {699-710},
title = {Ultra regular covering space and its automorphism group},
url = {http://eudml.org/doc/208019},
volume = {20},
year = {2010},
}

TY - JOUR
AU - Sang-Eon Han
TI - Ultra regular covering space and its automorphism group
JO - International Journal of Applied Mathematics and Computer Science
PY - 2010
VL - 20
IS - 4
SP - 699
EP - 710
AB - In order to classify digital spaces in terms of digital-homotopic theoretical tools, a recent paper by Han (2006b) (see also the works of Boxer and Karaca (2008) as well as Han (2007b)) established the notion of regular covering space from the viewpoint of digital covering theory and studied an automorphism group (or Deck's discrete transformation group) of a digital covering. By using these tools, we can calculate digital fundamental groups of some digital spaces and classify digital covering spaces satisfying a radius 2 local isomorphism (Boxer and Karaca, 2008; Han, 2006b; 2008b; 2008d; 2009b). However, for a digital covering which does not satisfy a radius 2 local isomorphism, the study of a digital fundamental group of a digital space and its automorphism group remains open. In order to examine this problem, the present paper establishes the notion of an ultra regular covering space, studies its various properties and calculates an automorphism group of the ultra regular covering space. In particular, the paper develops the notion of compatible adjacency of a digital wedge. By comparing an ultra regular covering space with a regular covering space, we can propose strong merits of the former.
LA - eng
KW - digital image; digital isomorphism; (ultra) regular covering space; digital covering space; simply k-connected; Deck's discrete transformation group; compatible adjacency; digital wedge; automorphism group; simply -connected
UR - http://eudml.org/doc/208019
ER -

References

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