Smooth Yamabe invariant and surgery

Bernd Ammann (1) , Mattias Dahl (2) , Emmanuel Humbert (3)

1 UNIVERSITAET REGENSBURG - Universitaet Regensburg
2 KTH STOCKHOLM - Institutionen för Matematik - KTH
3 IECL - Institut Élie Cartan de Lorraine

We prove a surgery formula for the smooth Yamabe invariant $\sigma(M)$ of a compact manifold $M$. Assume that $N$ is obtained from $M$ by surgery of codimension at least $3$. We prove the existence of a positive number $\Lambda_n$, depending only on the dimension $n$ of $M$, such that $$ \sigma(N) \geq \min\{\sigma(M),\Lambda_n\}. $$

Mots clés: positive scalar curvature; Yamabe operator; Yamabe invariant; surgery

Domaines: Géométrie différentielle [math.DG]

Bernd Ammann, Mattias Dahl, Emmanuel Humbert. Smooth Yamabe invariant and surgery. Journal of Differential Geometry, 2013, 94 (1), pp.1-58. ⟨hal-00271361v3⟩