Loop homological invariants associated to real projective spaces

Abstract

Let A be a based subspace of Y. Under the assumptions that Y is path-connected and that the reduced diagonal map of A induces the zero map in all mod 2 reduced homology groups, we compute a formula for the mod 2 reduced Poincaré series of the loop space $\Omega ((A\wedge {\mathbb{RP}}^{\infty }){\cup }_{A\wedge {\mathbb{RP}}^1}(Y\wedge {\mathbb{RP}}^1))$. Here ${\mathbb{RP}}^{\infty }$ and ${\mathbb{RP}}^1$ denote the infinite real projective space and the real projective line respectively.

References in corpus (2)

• The field Q(2cos(pi/n)), its Galois group and length ratios in the regular n-gon
• Homology Decompositions of the Loops on 1-Stunted Borel Constructions of C_2-Actions