Homotopy types of spaces of submanifolds of \mathbb Rⁿ

2014/12/16 by Federico Cantero Morán, Morán, Federico Cantero
Mathematics · Physics and Astronomy · #55P60 #55R25 #55R80 #Advanced Differential Geometry Research #Algebraic Topology (math.AT) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric Topology (math.GT) #Homotopy and Cohomology in Algebraic Topology #math.AT #math.GT #msc:55P60 #msc:55R25 #msc:55R80

paper · pdf · doi:10.48550/arxiv.1412.4938

15 pages. More detailed

openalex publication_date 2014/12/16 · arxiv created 2016/01/15 · arxiv updated 2016/01/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We compute the homotopy type of the space of proper d-dimensional submanifolds of \mathbb Rⁿ with a smooth version of the Fell topology. Our methods allow us to compute the homotopy type of the space of submanifolds with summable labels too, and to give a new proof of the Galatius--Randal-Williams theorem on the homotopy type of their space of submanifolds

Related

• On the rational homotopy type of embedding spaces of manifolds in Rⁿ
• Homotopy classes of proper maps out of vector bundles
• Moduli spaces of homotopy theory
• Presentation of homotopy types under a space
• Homotopy operations and rational homotopy type