Geodesic
Homotopy groups of highly connected Poincaré duality complexes
Documenta mathematica, Tome 27 (2022), pp. 183-211.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Methods are developed to relate the action of a principal fibration to relative Whitehead products in order to determine the homotopy type of certain spaces. The methods are applied to thoroughly analyze the homotopy type of the based loops on certain cell attachments. Key examples are $(n-1)$-connected Poincaré Duality complexes of dimension $2n$ or $2n+1$ with minor cohomological conditions.
Classification : 55P35, 57N65, 55Q15
Keywords: principal fibration, Whitehead product, loop space decomposition, Poincaré duality complex 
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     author = {Beben, Piotr and Theriault, Stephen},
     title = {Homotopy groups of highly connected {Poincar\'e} duality complexes},
     journal = {Documenta mathematica},
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     volume = {27},
     year = {2022},
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Beben, Piotr; Theriault, Stephen. Homotopy groups of highly connected Poincaré duality complexes. Documenta mathematica, Tome 27 (2022), pp. 183-211. http://geodesic.mathdoc.fr/item/DOCMA_2022__27__a62/