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

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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.
DOI : 10.4171/dm/869
Classification : 55P35, 55Q15, 57N65
Mots-clés : principal fibration, Whitehead product, loop space decomposition, Poincaré duality complex 
Piotr Beben; Stephen Theriault. Homotopy groups of highly connected Poincaré duality complexes. Documenta mathematica, Tome 27 (2022), pp. 183-211. doi: 10.4171/dm/869
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     author = {Piotr Beben and Stephen Theriault},
     title = {Homotopy groups of highly connected {Poincar\'e} duality complexes},
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     volume = {27},
     doi = {10.4171/dm/869},
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