Regular embeddings of manifolds and topology of configuration spaces

2010/06/03 by Роман Карасев, R. N. Karasev, Karasev, R. N.
Computer Science · Mathematics · #41A50 #55M35 #55R25 #55R80 #57R40 #Algebraic Topology (math.AT) #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Topological and Geometric Data Analysis #math.AT #math.GT #msc:41A50 #msc:55M35 #msc:55R25 #msc:55R80 #msc:57R40

paper · pdf · doi:10.48550/arxiv.1006.0613

openalex publication_date 2010/06/03 · arxiv created 2011/06/28 · arxiv updated 2011/06/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For a topological space X we study continuous maps f : X→ \mathbb R^m such that images of every pairwise distinct k points are affinely (linearly) independent. Such maps are called affinely (linearly) k-regular embeddings. We investigate the cohomology obstructions to existence of regular embeddings and give some new lower bounds on the dimension m as function of X and k, for the cases X is \mathbb Rⁿ or X is an n-dimensional manifold. In the latter case, some nonzero Stiefel--Whitney classes of X help to improve the bound.

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