Elsevier

Advances in Mathematics

Volume 205, Issue 1, 10 September 2006, Pages 84-133
Advances in Mathematics

Orbifold genera, product formulas and power operations

https://doi.org/10.1016/j.aim.2005.07.005Get rights and content
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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. Math. Phys. 185(1) (1997) 197–209]. It depends only on h and not on the genus.

MSC

55N34
58J26
55P42

Keywords

Orbifold genus
K(h)-local category
Elliptic cohomology

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