A CERTAIN OPEN MANIFOLD WHOSE GROUP IS UNITY

1962 ◽  
pp. 39-50 ◽  
Keyword(s):  
Open Manifold

scholarly journals Normal subgroups of diffeomorphism and homeomorphism groups of ℝn and other open manifolds

2011 ◽  
Vol 31 (6) ◽  
pp. 1835-1847 ◽  
Author(s):  
PAUL A. SCHWEITZER, S. J.
Keyword(s):  
Normal Subgroup ◽  
Compact Manifold ◽  
Normal Subgroups ◽  
Open Manifold ◽  
Open Manifolds ◽  
Group Of Homeomorphisms ◽  
Homeomorphism Groups

AbstractWe determine all the normal subgroups of the group of Cr diffeomorphisms of ℝn, 1≤r≤∞, except when r=n+1 or n=4, and also of the group of homeomorphisms of ℝn ( r=0). We also study the group A0 of diffeomorphisms of an open manifold M that are isotopic to the identity. If M is the interior of a compact manifold with non-empty boundary, then the quotient of A0 by the normal subgroup of diffeomorphisms that coincide with the identity near to a given end e of M is simple.

scholarly journals The topology of an open manifold with radial curvature bounded from below by a model surface with finite total curvature and examples of model surfaces

2013 ◽  
Vol 209 ◽  
pp. 23-34 ◽  
Author(s):  
Minoru Tanaka ◽  
Kei Kondo
Keyword(s):  
Total Curvature ◽  
Comparison Theorems ◽  
Surfaces Of Revolution ◽  
Model Surface ◽  
Open Manifold ◽  
Finite Total Curvature ◽  
Radial Curvature ◽  
Noncompact Riemannian Manifold ◽  
Sectional Curvatures ◽  
Noncompact Riemannian Manifolds

AbstractWe construct distinctive surfaces of revolution with finite total curvature whose Gauss curvatures are not bounded. Such a surface of revolution is employed as a reference surface of comparison theorems in radial curvature geometry. Moreover, we prove that a complete noncompact Riemannian manifold M is homeomorphic to the interior of a compact manifold with boundary if the manifold M is not less curved than a noncompact model surface of revolution and if the total curvature of the model surface is finite and less than 2π. By the first result mentioned above, the second result covers a much wider class of manifolds than that of complete noncompact Riemannian manifolds whose sectional curvatures are bounded from below by a constant.

scholarly journals Open manifolds with non-homeomorphic positively curved souls

2019 ◽  
Vol 169 (2) ◽  
pp. 357-376 ◽  
Author(s):  
DAVID GONZÁLEZ-ÁLVARO ◽  
MARCUS ZIBROWIUS
Keyword(s):  
Sectional Curvature ◽  
Existence Results ◽  
Positive Answer ◽  
Open Manifold ◽  
Positive Sectional Curvature ◽  
Open Manifolds ◽  
Curved Manifolds ◽  
Eschenburg Spaces ◽  
Simply Connected ◽  
Positively Curved

AbstractWe extend two known existence results to simply connected manifolds with positive sectional curvature: we show that there exist pairs of simply connected positively-curved manifolds that are tangentially homotopy equivalent but not homeomorphic, and we deduce that an open manifold may admit a pair of non-homeomorphic simply connected and positively-curved souls. Examples of such pairs are given by explicit pairs of Eschenburg spaces. To deduce the second statement from the first, we extend our earlier work on the stable converse soul question and show that it has a positive answer for a class of spaces that includes all Eschenburg spaces.

On Contractible Open Manifolds

1962 ◽  
Vol 58 (2) ◽  
pp. 221-224 ◽  
Author(s):  
D. R. McMillan ◽  
E. C. Zeeman
Keyword(s):  
Compact Space ◽  
Open Manifold ◽  
Open Manifolds ◽  
Combinatorial Manifold

By an open manifold we mean a non-compact space, that is triangulable by a countable complex which is a combinatorial manifold without boundary (see next section).

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