Geodesic
Generalized orbifold Euler characteristic of symmetric products and equivariant Morava K–theory
Tamanoi, Hirotaka1
1Department of Mathematics, University of California Santa Cruz, Santa Cruz CA 95064, USA
Algebraic and Geometric Topology, Tome 1 (2001) no. 1, pp. 115-141
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We introduce the notion of generalized orbifold Euler characteristic associated to an arbitrary group, and study its properties. We then calculate generating functions of higher order (p–primary) orbifold Euler characteristic of symmetric products of a G–manifold M. As a corollary, we obtain a formula for the number of conjugacy classes of d–tuples of mutually commuting elements (of order powers of p) in the wreath product G ≀ Sn in terms of corresponding numbers of G. As a topological application, we present generating functions of Euler characteristic of equivariant Morava K–theories of symmetric products of a G–manifold M.

DOI : 10.2140/agt.2001.1.115
Keywords: equivariant Morava K-theory, generating functions, $G$-sets, Möbius functions, orbifold Euler characteristics, q-series, second quantized manifolds, symmetric products, twisted iterated free loop space, twisted mapping space, wreath products, Riemann zeta function

Tamanoi, Hirotaka  1

1 Department of Mathematics, University of California Santa Cruz, Santa Cruz CA 95064, USA 
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Tamanoi, Hirotaka. Generalized orbifold Euler characteristic of symmetric products and equivariant Morava K–theory. Algebraic and Geometric Topology, Tome 1 (2001) no. 1, pp. 115-141. doi: 10.2140/agt.2001.1.115

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