Classification of the crossed product C(m) × θZp for certain pairs (M, θ) | Zendy

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Classification of the crossed product C(m) × θZp for certain pairs (M, θ)

Author(s) -

Yifeng Xue

Publication year - 2010

Publication title -

filomat

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.449

H-Index - 34

eISSN - 2406-0933

pISSN - 0354-5180

DOI - 10.2298/fil1002131x

Subject(s) - mathematics , homeomorphism (graph theory) , combinatorics , separable space , hausdorff space , prime (order theory) , product (mathematics) , prime number , mathematical analysis , geometry

Let M be a separable compact Hausdorff space with dim M ? 2 and ? : M ? M be a homeomorphism with prime period p (p ? 2). Set M? = {x ( M|?(x) = x} = ( and M0 = M\M? . Suppose that M0 is dense in M and H2(M0/?, Z) ( 0, H2(?(M0/?), Z) ( 0. Let M' be another separable compact Hausdorff space with dim M' ? 2 and ?' be the self-homeomorphism of M' with prime period p. Suppose that M'0 = M'\M'?' is dense in M'. Then C(M) ? ?Zp ( C(M') ? ?'Zp if there is a homeomorphism F from M/? onto M'/?' such that F(M?) = M'?'. Thus, if (M, ?) and (M', ?') are orbit equivalent, then C(M) ? ?Zp ( C(M') ? ?'Zp. 2010 Mathematics Subject Classifications. 46L05. .

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