Orbifold genera, product formulas and power operations

Details Orbifold genera, product formulas and power operations Orbifold genera, product formulas and power operations

2004-07-01

arxiv.org/abs/math/0407021v2

Adv. Math. 205 (2006), no. 1, 84-133

Mathematics

Algebraic Topology

36 pages, PhD thesis, revised version

Scientific paper

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-infinity-map into the Morava-Lubin-Tate theory E_h, 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. It depends only on h and not on the genus.

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