Following a Bendersky-Gitler idea, we construct an isomorphism between Anderson’s and Arone’s complexes modelling the chain complex of a mapping space. This allows us to apply Shipley’s convergence theorem to Arone’s model. As a corollary, we reduce the problem of homotopy equivalence for certain “toy” spaces to a problem in homological algebra.
@article{bwmeta1.element.doi-10_2478_s11533-011-0084-1,
author = {Sem\"en Podkorytov},
title = {On the homology of mapping spaces},
journal = {Open Mathematics},
volume = {9},
year = {2011},
pages = {1232-1241},
zbl = {1236.55023},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-011-0084-1}
}
Semën Podkorytov. On the homology of mapping spaces. Open Mathematics, Tome 9 (2011) pp. 1232-1241. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-011-0084-1/
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