Journal article

Orbifold genera, product formulas and power operations

Nora Ganter

ADVANCES IN MATHEMATICS | ACADEMIC PRESS INC ELSEVIER SCIENCE | Published : 2006

Abstract

We generalize the definition of orbifold elliptic genus and introduce orbifold genera of chromatic level h, using h-tuples rather than pairs of commuting elements. We show that our genera are in fact orbifold invariants, and we prove integrality results for them. If the genus arises from an H∞-map into the Morava-Lubin-Tate theory Eh, then we give a formula expressing the orbifold genus of the symmetric powers of a stably almost complex manifold M in terms of the genus of M itself. Our formula is the p-typical analogue of the Dijkgraaf-Moore-Verlinde-Verlinde formula for the orbifold elliptic genus [R. Dijkgraaf et al., Elliptic genera of symmetric products and second quantized strings Comm...

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