EMIS/ELibM Electronic Journals

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These pages are not updated anymore. They reflect the state of 6 June 2010. For the current production of this journal, please refer to http://www.springer.com/mathematics/geometry/journal/40062.

A rational obstruction to be a Gottlieb map

A rational obstruction to be a Gottlieb map

Toshihiro Yamaguchi

We investigate {\it Gottlieb map}s,which are maps $f:E\to B$that induce the maps betweenthe Gottlieb groups$\pi_n (f)|_{G_n(E)}:G_n(E)\to G_n(B)$ for all $n$,from a rational homotopy theory point of view. We will define the obstruction group $O(f)$to be a Gottlieb map and a numerical invariant $o(f)$. It naturally deduces a relative splittingof $E$ in certain cases. We also illustrate several rational examples of Gottlieb maps and non-Gottlieb mapsby using derivation arguments in Sullivan models.

Journal of Homotopy and Related Structures, Vol. 5(2010), No. 1, pp. 97-111