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Harmonic and Minimal Unit Vector Fields on the Symmetric Spaces G 2 and G 2 / S O ( 4 )

László Verhóczki (2012)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

The exceptional compact symmetric spaces G 2 and G 2 / S O ( 4 ) admit cohomogeneity one isometric actions with two totally geodesic singular orbits. These singular orbits are not reflective submanifolds of the ambient spaces. We prove that the radial unit vector fields associated to these isometric actions are harmonic and minimal.

Higher simple structure sets of lens spaces with the fundamental group of arbitrary order

L’udovít Balko, Tibor Macko, Martin Niepel, Tomáš Rusin (2019)

Archivum Mathematicum

Extending work of many authors we calculate the higher simple structure sets of lens spaces in the sense of surgery theory with the fundamental group of arbitrary order. As a corollary we also obtain a calculation of the simple structure sets of the products of lens spaces and spheres of dimension grater or equal to 3 .

Homeomorphism Groups and the Topologist's Sine Curve

Jan J. Dijkstra, Rachid Tahri (2010)

Bulletin of the Polish Academy of Sciences. Mathematics

It is shown that deleting a point from the topologist's sine curve results in a locally compact connected space whose autohomeomorphism group is not a topological group when equipped with the compact-open topology.

Homeomorphism groups of Sierpiński carpets and Erdős space

Jan J. Dijkstra, Dave Visser (2010)

Fundamenta Mathematicae

Erdős space is the “rational” Hilbert space, that is, the set of vectors in ℓ² with all coordinates rational. Erdős proved that is one-dimensional and homeomorphic to its own square × , which makes it an important example in dimension theory. Dijkstra and van Mill found topological characterizations of . Let M n + 1 , n ∈ ℕ, be the n-dimensional Menger continuum in n + 1 , also known as the n-dimensional Sierpiński carpet, and let D be a countable dense subset of M n + 1 . We consider the topological group ( M n + 1 , D ) of all...

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