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The $n$ -fold product $X^{n}$ of an arbitrary space usually supports only the obvious permutation action of the symmetric group $Σ_{n}$ . However, if $X$ is a $p$ -complete, homotopy associative, homotopy commutative $H$ -space one can define a homotopy action of ${GL}_{n} (ℤ_{p})$ on $X^{n}$ . In various cases, e.g. if multiplication by $p^{r}$ is null homotopic then we get a homotopy action of $G L_{n} (ℤ / p^{r})$ for some $r$ . After one suspension this allows one to split $X^{n}$ using idempotents of $𝔽_{p} {GL}_{n} (ℤ / p)$ which can be lifted to $𝔽_{p} {GL}_{n} (ℤ / p^{r})$ . In fact all of this is possible if $X$ is an $H$ -space...

On co-H-spaces.

G. Mislin, Peter Hilton, J. Roitberg (1978)

Commentarii mathematici Helvetici

On compact symplectic and Kählerian solvmanifolds which are not completely solvable

Aleksy Tralle (1997)

Colloquium Mathematicae

We are interested in the problem of describing compact solvmanifolds admitting symplectic and Kählerian structures. This was first considered in [3, 4] and [7]. These papers used the Hattori theorem concerning the cohomology of solvmanifolds hence the results obtained covered only the completely solvable case}. Our results do not use the assumption of complete solvability. We apply our methods to construct a new example of a compact symplectic non-Kählerian solvmanifold.

On components of MANR-spaces

Stanisław Godlewski (1981)

Fundamenta Mathematicae

On constructing resolutions over the polynomial algebras.

Johansson, Leif, Lambe, Larry, Sköldberg, Emil (2002)

Homology, Homotopy and Applications

On Davis-Januszkiewicz homotopy types I: formality and rationalisation.

Notbohm, Dietrich, Ray, Nigel (2005)

Algebraic & Geometric Topology

On deformations of spherical isometric foldings

Ana M. Breda, Altino F. Santos (2010)

Czechoslovak Mathematical Journal

The behavior of special classes of isometric foldings of the Riemannian sphere $S^{2}$ under the action of angular conformal deformations is considered. It is shown that within these classes any isometric folding is continuously deformable into the standard spherical isometric folding $f_{s}$ defined by $f_{s} (x, y, z) = (x, y, | z |)$ .

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