Sobolev maps on manifolds: degree, approximation, lifting

Petru Mironescu (1)

1 EDPA - Équations aux dérivées partielles, analyse

In this paper, we review some basic topological properties of the space $X = W^{s,p}(M ; N)$, where $M$ and $N$ are compact Riemannian manifold without boundary. More specifically, we discuss the following questions: can one define a degree for maps in $X$? Are smooth or not-far-from-being-smooth maps dense in $X$? Can one lift ${\mathbb S}^1$-valued maps?

Mots clés: approximation; Sobolev spaces; compact manifolds; degree; lifting

Domaines: Analyse classique [math.CA]

Petru Mironescu. Sobolev maps on manifolds: degree, approximation, lifting. Contemporary mathematics, 2007, 446 (Perspectives in nonlinear partial differential equations), pp.413-436. ⟨10.1090/conm/446/08642⟩. ⟨hal-00747679⟩