Enlargeability, foliations, and positive scalar curvature

Moulay Benameur (1) , James L. Heitsch (2)

1 IMAG - Institut Montpelliérain Alexander Grothendieck
2 Mathematics, Statistics, and Computer Science

We extend the deep and important results of Lichnerowicz, Connes, and Gromov-Lawson which relate geometry and characteristic numbers to the existence and non-existence of metrics of positive scalar curvature. In particular, we show that a spin foliation with Hausdorff homotopy groupoid of an enlargeable manifold admits no metric of positive scalar curvature.

Domaines: Topologie géométrique [math.GT]

Moulay Benameur, James L. Heitsch. Enlargeability, foliations, and positive scalar curvature. Inventiones Mathematicae, 2019, 215 (1), pp.367-382. ⟨10.1007/s00222-018-0829-6⟩. ⟨hal-01819124⟩