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On manifolds homotopy equivalent to the total spaces of S 7 -bundles over S 8

Ajay Raj, Tibor Macko (2024)

Archivum Mathematicum

We calculate the structure sets in the sense of surgery theory of total spaces of bundles over eight-dimensional sphere with fibre a seven-dimensional sphere, in which manifolds homotopy equivalent to the total spaces are organized, and we investigate the question, which of the elements in these structure sets can be realized as such bundles.

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 pseudo-isotopy classes of homeomorphisms of a dimensional differentiable manifold.

Alberto Cavicchioli, Friedrich Hegenbarth (1998)

Revista Matemática Complutense

We study self-homotopy equivalences and diffeomorphisms of the (n+1)-dimensional manifold X= #p(S1 x Sn) for any n ≥ 3. Then we completely determine the group of pseudo-isotopy classes of homeomorphisms of X and extend to dimension n well-known theorems due to F. Laudenbach and V. Poenaru (1972,1973), and J. M. Montesinos (1979).

On real flag manifolds with cup-length equal to its dimension

Marko Radovanović (2020)

Czechoslovak Mathematical Journal

We prove that for any positive integers n 1 , n 2 , ... , n k there exists a real flag manifold F ( 1 , ... , 1 , n 1 , n 2 , ... , n k ) with cup-length equal to its dimension. Additionally, we give a necessary condition that an arbitrary real flag manifold needs to satisfy in order to have cup-length equal to its dimension.

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