Algebraic & Geometric Topology

Generalized orbifold Euler characteristic of symmetric products and equivariant Morava K–theory

Hirotaka Tamanoi

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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 GSn 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.

Article information

Algebr. Geom. Topol., Volume 1, Number 1 (2001), 115-141.

Received: 29 October 2000
Revised: 16 February 2001
Accepted: 16 February 2001
First available in Project Euclid: 21 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 55N20: Generalized (extraordinary) homology and cohomology theories 55N91: Equivariant homology and cohomology [See also 19L47]
Secondary: 57S17: Finite transformation groups 57D15 20E22: Extensions, wreath products, and other compositions [See also 20J05] 37F20: Combinatorics and topology 05A15: Exact enumeration problems, generating functions [See also 33Cxx, 33Dxx]

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. Generalized orbifold Euler characteristic of symmetric products and equivariant Morava K–theory. Algebr. Geom. Topol. 1 (2001), no. 1, 115--141. doi:10.2140/agt.2001.1.115.

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