On a formula for the asymptotic dimension of free products

Tom 183 / 2004

G. C. Bell, A. N. Dranishnikov, J. E. Keesling Fundamenta Mathematicae 183 (2004), 39-45 MSC: Primary 20F69; Secondary 20E08, 20E06. DOI: 10.4064/fm183-1-2

Streszczenie

We prove an exact formula for the asymptotic dimension (asdim) of a free product. Our main theorem states that if $A$ and $B$ are finitely generated groups with $\mathop {\rm asdim}\nolimits A=n$ and $\mathop {\rm asdim}\nolimits B\le n$, then ${\rm asdim} (A\ast B)=\mathop {\rm max} \{n,1\}.$

Autorzy

  • G. C. BellDepartment of Mathematics
    The Pennsylvania State University
    University Park, PA 16802, U.S.A.
    e-mail
  • A. N. DranishnikovDepartment of Mathematics
    University of Florida
    358 Little Hall
    P.O. Box 118105
    Gainesville, FL 32611-8105, U.S.A.
    e-mail
  • J. E. KeeslingDepartment of Mathematics
    University of Florida
    358 Little Hall
    P.O.Box 118105
    Gainesville, FL, 32611-8105, U.S.A.
    e-mail

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