# Twisted homology of configuration spaces, homology of spaces of equivariant maps, and stable homology of spaces of non-resultant systems of real homogeneous polynomials

@article{Vassiliev2018TwistedHO, title={Twisted homology of configuration spaces, homology of spaces of equivariant maps, and stable homology of spaces of non-resultant systems of real homogeneous polynomials}, author={Victor A. Vassiliev}, journal={arXiv: Algebraic Topology}, year={2018} }

A spectral sequence calculating the homology groups of some spaces of maps equivariant under finite group actions is described. For the main example, We calculate the rational homology groups of spaces of even and odd maps $S^m \to S^M$, $m<M$, or, which is the same, the stable homology groups of spaces of non-resultant homogeneous polynomial maps ${\mathbb R}^{m+1} \to {\mathbb R}^{M+1}$ of growing degrees. Also, we find the homology groups of spaces of ${\mathbb Z}_r$-equivariant maps of odd…

## One Citation

### Cohomology of spaces of Hopf equivariant maps of spheres

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- 2021

For any natural k ≤ n, the rational cohomology ring of the space of continuous maps S → S (respectively, S → S) equivariant under the Hopf action of the circle (respectively, of the group S of unit…

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