Proceedings of the International Geometry Center

ISSN-print: 2072-9812
ISSN-online: 2409-8906
ISO: 26324:2012
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Relative Gottlieb groups of mapping spaces and their rational cohomology

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Abdelhadi Zaim

Abstract

Let f:X →Y be a map of simply connected CW-complexes of finite type. Put maxπ(Y)⊗Q = max{ i | πi(Y)⊗Q≠0 }. In this paper we compute the relative Gottlieb groups of f when X is an F0-space and Y is a product of odd spheres. Also, under reasonable hypothesis, we determine these groups when X is a product of odd spheres and Y is an F0-space. As a consequence, we show that the rationalized G-sequence associated to f splits into a short exact sequence. Finally, we prove that the rational cohomology of map(X,Y;f) is infinite dimensional whenever maxπ(Y)⊗Q is even.

Keywords:
rational homotopy theory, Sullivan minimal model, Gottlieb groups, relative Gottlieb groups, rational cohomology

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How to Cite
Zaim, A. (2022). Relative Gottlieb groups of mapping spaces and their rational cohomology. Proceedings of the International Geometry Center, 15(1), 1-15. https://doi.org/10.15673/tmgc.v15i1.2196
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Papers