Orbifold elliptic genera and rigidity. (English) Zbl 1158.57034

Hattori, Akio

J. Math. Soc. Japan 58, No. 2, 419-452 (2006).

A modified orbifold elliptic genus of level \(N\) is defined for closed almost complex orbifolds such that \(N\) is relatively prime to the orders of all isotopy groups. It is proved that the modified orbifold elliptic genus of level \(N\) of an almost complex orbifold \(X\) of dimension \(2n\) such that \(\Lambda^nTX=L^N\) for some orbifold line bundle \(L\) is rigid for a non-trivial \(G\) action. Another important theorem states that this orbifold elliptic genus of level \(N\) of \(X\) is rigid for a non-trivial \(G\) action if \(\Lambda^nTX=L^N\) for some genuine \(G\) line bundle \(L\).

Reviewer: Gheorghe Pitiş (Braşov)

MSC:

57R20	Characteristic classes and numbers in differential topology
57S15	Compact Lie groups of differentiable transformations
55N34	Elliptic cohomology
55N91	Equivariant homology and cohomology in algebraic topology

Keywords:

orbifold; elliptic genus; orbifold elliptic genus; \(T_y\)–genus; rigidity theorem; vanishing theorem