Sobolev mappings, degree, homotopy classes and rational homology spheres

2011/09/22 by Paweł Goldstein, Pawel Goldstein, Piotr Hajłasz +3
Mathematics · #Algebraic Topology (math.AT) #FOS: Mathematics #Functional Analysis (math.FA) #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Nonlinear Partial Differential Equations #Primary 46E35 #Secondary 46E30 #math.AT #math.FA #msc:46E30 #msc:46E35

paper · pdf · doi:10.48550/arxiv.1109.4831

arxiv created 2011/09/22 · openalex publication_date 2011/09/22 · arxiv updated 2011/09/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

In the paper we investigate the degree and the homotopy theory of Orlicz-Sobolev mappings W^1,P(M,N) between manifolds, where the Young function P satisfies a divergence condition and forms a slightly larger space than W^1,n, n=dim M. In particular, we prove that if M and N are compact oriented manifolds without boundary and dim M=dim N=n, then the degree is well defined in W^1,P(M,N) if and only if the universal cover of N is not a rational homology sphere, and in the case n=4, if and only if N is not homeomorphic to S⁴.

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