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Simplicial resolutions and Ganea fibrations

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Thomas Kahl, Hans Scheerer, Daniel Tanré and Lucile Vandembroucq

In this work, we compare two approximations of a path-connected space $X$:
the one given bythe Ganea spaces $G_n(X)$ and the one given by the realizations
$\|\Lambda_\bullet X\|_{n}$ of the truncated simplicial resolutions induced by
the loop-suspen\-sion co\-triple $\Sigma\Omega$.For a simply connected space
$X$, we construct maps
$\|\Lambda_\bullet X\|_{n-1}\to G_n(X)\to \|\Lambda_\bullet X\|_{n}$ over $X$,
up to homotopy.In the case $n=2$, we also prove the existence of a
map$G_2(X)\to\|\Lambda_\bullet X\|_{1}$ over $X$ (up to homotopy).

Journal of Homotopy and Related Structures, Vol. 3(2008), No. 1, pp. 309-330