Cohomology of spaces of Hopf equivariant maps of spheres

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Cohomology of spaces of Hopf equivariant maps of spheres

Homology, Homotopy and Applications. 2024. Vol. 26. No. 2. P. 219–227.

The rational cohomology ring of the space of maps of spheres equivariant under the Hopf action of the circle is isomorphic to that of a complex Stiefel manifold

Language: English

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Traces of weighted Sobolev spaces with Muckenhoupt weight. The case $p=1$.

Tyulenev A., Nonlinear Analysis, Theory, Methods and Applications 2015 Vol. 128 P. 248–272

Added: December 25, 2025

On the homology of spaces of equivariant maps

Vassiliev V., Journal of Topology and Analysis 2024 Vol. 16 No. 4 P. 461–494

A general method of computing the cohomology groups of spaces of equivariant maps is developed and applied to the spaces of odd and even maps of spheres ...

Added: October 31, 2025

Uniformly convergent Fourier series and multiplication of functions

V. V. Lebedev, Proceedings of the Steklov Institute of Mathematics 2018 Vol. 303 P. 171–177

Let U(T) be the space of all continuous functions on the circle T whose Fourier series converges uniformly. Salem’s well-known example shows that a product of two functions in U(T) does not always belong to U(T) even if one of the factors belongs to the Wiener algebra A(T). In this paper we consider pointwise multipliers ...

Added: February 21, 2019

Twisted homology of configuration spaces and homology of spaces of equivariant maps

V.A.Vassiliev, Doklady Mathematics (Springer, Germany) 2018 Vol. 98 No. 3 P. 629–633

We calculate homology groups with certain twisted coefficients of configuration spaces of projective spaces. This completes a calculation of rational homology groups of spaces of odd maps of spheres S^m \to S^M, m<M, and of the stable homology of spaces of non-resultant polynomial maps R^{m+1} -> R^{M+1}. Also, we calculate the homology of spaces of Z_r-equivariant maps ...

Added: January 9, 2019

Uniformly convergent Fourier series and multiplication of functions

V. V. Lebedev, / Series math "arxiv.org". 2018. No. arXiv:1807.03949v1.

Let U(T) be the space of all continuous functions on the circle T whose Fourier series converges uniformly. Salem's well-known example shows that a product of two functions in U(T) does not always belongs to U(T) even if one of the factors belongs to the Wiener algebra A(T). In this paper we consider pointwise multipliers of the space U(T), i.e., the functions ...

Added: July 12, 2018