The suspended free loop space of a symmetric space

2005/11/03 by Marcel Bökstedt, Bokstedt, Marcel, Iver Ottosen +1 · 1 citation
Mathematics · Physics and Astronomy · #53C35 #55P35 #55P42 #58E05 #Advanced Differential Geometry Research #Algebraic Topology (math.AT) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Mathematics and Applications

paper · pdf · doi:10.48550/arxiv.math/0511086

openalex publication_date 2005/11/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let M be one of the projective spaces CPⁿ, HPⁿ for n>1 or the Cayley projective plane OP², and let LM denote the free loop space on M. Using Morse theory methods, we prove that the suspension spectrum of (LM)₊ is homotopy equivalent to the suspension spectrum of M₊ wedge a family of Thom spaces of explicit vector bundles over the tangent sphere bundle of M.

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• Loop homology of quaternionic projective spaces

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