Orbifold index cobordism invariance (Q1030177)

The statement of the main result of this article is that for two closed orbifolds which are locally free quotients of actions of a compact Lie group \(G\) on smooth closed manifolds and for elliptic pseudo-differentail operators on them, their orbifold symbol cobordance implies index equality for those operators. As for the proof, one ingredient is the push-forward property of the transverse index under \(G\)-embeddings, established by \textit{M. F. Atiyah} [``Elliptic operators and compact groups'', Lect. Notes Math. 401 (1974; Zbl 0297.58009)], and the other is the \(K\)-theoretical proof by Carvalho for the invariance of transversally elliptic operators. The contents consist of Atiyah distributional transverse index, restriction and boundary maps together with symbol \(G\)-cobordism, properties of the index, restriction, and boundary maps with respect to \(G\)-equivariant embeddings, and the proof of the main result.