Geodesic
𝒵–Structures on product groups
Tirel, Carrie J1
1Department of Mathematics, University of Wisconsin - Fox Valley, 1478 Midway Rd, Menasha WI 54952, USA
Algebraic and Geometric Topology, Tome 11 (2011) no. 5, pp. 2587-2625
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A Z–structure on a group G, defined by M Bestvina, is a pair (X̂,Z) of spaces such that X̂ is a compact ER, Z is a Z–set in X̂, G acts properly and cocompactly on X = X̂∖Z and the collection of translates of any compact set in X forms a null sequence in X̂. It is natural to ask whether a given group admits a Z–structure. In this paper, we show that if two groups each admit a Z–structure, then so do their free and direct products.

DOI : 10.2140/agt.2011.11.2587
Classification : 57M07, 20F65
Keywords: $\mathcal{Z}$–structure, boundary, free product, direct product, product group

Tirel, Carrie J  1

1 Department of Mathematics, University of Wisconsin - Fox Valley, 1478 Midway Rd, Menasha WI 54952, USA 
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Tirel, Carrie J. 𝒵–Structures on product groups. Algebraic and Geometric Topology, Tome 11 (2011) no. 5, pp. 2587-2625. doi: 10.2140/agt.2011.11.2587

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