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On manifolds with nonhomogeneous factors

Manuel Cárdenas, Francisco Lasheras, Antonio Quintero, Dušan Repovš (2012)

Open Mathematics

We present simple examples of finite-dimensional connected homogeneous spaces (they are actually topological manifolds) with nonhomogeneous and nonrigid factors. In particular, we give an elementary solution of an old problem in general topology concerning homogeneous spaces.

On the connectedness of boundary and complement for domains

Andrzej Czarnecki, Marcin Kulczycki, Wojciech Lubawski (2011)

Annales Polonici Mathematici

This article gives a short and elementary proof of the fact that the connectedness of the boundary of an open domain in ℝⁿ is equivalent to the connectedness of its complement.

On the exponent of the cokernel of the forget-control map on K₀-groups

Francis X. Connolly, Stratos Prassidis (2002)

Fundamenta Mathematicae

For groups that satisfy the Isomorphism Conjecture in lower K-theory, we show that the cokernel of the forget-control K₀-groups is composed by the NK₀-groups of the finite subgroups. Using this information, we can calculate the exponent of each element in the cokernel in terms of the torsion of the group.

On the topological structure of compact 5-manifolds

Alberto Cavicchioli, Fulvia Spaggiari (1993)

Commentationes Mathematicae Universitatis Carolinae

We classify the genus one compact (PL) 5-manifolds and prove some results about closed 5-manifolds with free fundamental group. In particular, let M be a closed connected orientable smooth 5 -manifold with free fundamental group. Then we prove that the number of distinct smooth 5 -manifolds homotopy equivalent to M equals the 2 -nd Betti number (mod 2 ) of M .

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