scholarly journals Generalized universal covering spaces and the shape group

2007 ◽  
Vol 197 ◽  
pp. 167-196 ◽  
Author(s):  
Hanspeter Fischer ◽  
Andreas Zastrow
Keyword(s):  
Universal Covering ◽  
Covering Spaces ◽  
Shape Group

scholarly journals A presentation for a group of automorphisms of a simplicial complex

1988 ◽  
Vol 30 (3) ◽  
pp. 331-337 ◽  
Author(s):  
M. A. Armstrong
Keyword(s):  
Simplicial Complex ◽  
Elementary Proof ◽  
Universal Covering ◽  
Covering Space ◽  
Covering Spaces ◽  
Group Of Automorphisms ◽  
Generators And Relations ◽  
Universal Covering Space ◽  
Simply Connected ◽  
Special Case

The Bass–Serre theorem supplies generators and relations for a group of automorphisms of a tree. Recently K. S. Brown [2] has extended the result to produce a presentation for a group of automorphisms of a simply connected complex, the extra ingredient being relations which come from the 2-cells of the complex. Suppose G is the group, K the complex and L the 1-skeleton of K. Then an extension of π1(L) by G acts on the universal covering space of L (which is of course a tree) and Brown's technique is to apply the work of Bass and Serre to this action. Our aim is to give a direct elementary proof of Brown's theorem which makes no use of covering spaces, deals with the Bass–Serre theorem as a special case and clarifies the roles played by the various generators and relations.

scholarly journals A note on the variation of Riemann surfaces

1996 ◽  
Vol 142 ◽  
pp. 1-4 ◽  
Author(s):  
Takeo Ohsawa
Keyword(s):  
Riemann Surface ◽  
Complex Plane ◽  
Unit Disc ◽  
Riemann Surfaces ◽  
Riemann Sphere ◽  
Universal Covering ◽  
Covering Space ◽  
Uniformization Theorem ◽  
Covering Spaces ◽  
Universal Covering Space

Let X be any Riemann surface. By Koebe’s uniformization theorem we know that the universal covering space of X is conformally equivalent to either Riemann sphere, complex plane, or the unit disc in the complex plane. If X is allowed to vary with parameters we may inquire the parameter dependence of the corresponding family of the universal covering spaces.

scholarly journals A Remark on Differentiable Structures on Real Projective (2n-1)-Spaces

1966 ◽  
Vol 27 (1) ◽  
pp. 357-360 ◽  
Author(s):  
Kenichi Shiraiwa
Keyword(s):  
Universal Covering ◽  
Connected Sum ◽  
Covering Spaces ◽  
The Real

The main objective of this paper is to study the action of the group of differentiate structures Γ2n-1 on the (2n-1)-sphere S2n-1 on the diffeomorphism classes on the real projective (2n-1)-space P2n-1 by connected sum. This is done by considering universal covering spaces of the connected sum where Σ is an exotic (2n-1)-sphere.

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