Twisted homology of configuration spaces, homology of spaces of equivariant maps, and stable homology of spaces of nonresultant systems of real homogeneous polynomials
Abstract
A spectral sequence calculating the homology groups of some spaces of maps equivariant under compact 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 nonresultant 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 odddimensional spheres for any $r$. As a technical tool, we calculate the homology groups of configuration spaces of projective and lens spaces with coefficients in certain local systems.
 Publication:

arXiv eprints
 Pub Date:
 September 2018
 arXiv:
 arXiv:1809.05632
 Bibcode:
 2018arXiv180905632V
 Keywords:

 Mathematics  Algebraic Topology;
 55T99;
 14P25