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We study the set of critical exponents of discrete groups acting on regular trees. We prove that for every real number $\delta$ between $0$ and $\frac{1}{2}\log q$, there is a discrete subgroup $\Gamma$ acting without inversion on a $(q+1)$-regular tree whose critical exponent is equal to $\delta$. Explicit construction of edge-indexed graphs corresponding to a quotient graph of groups are given.
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참고문헌 (11)
참고문헌 신청
H. Bass / 1992 / The Ihara-Selberg zeta function of a tree lattice / Internat. J. Math 3(6):717~797
H. Bass / 1993 / Covering theory for graphs of groups / J. Pure Appl. Algebra 89(1-2):3~47
H. Bass / 1990 / Uniform tree lattices / J. Amer. Math. Soc 3(4):843~902
R. Coulon / Growth gap in hyperbolic groups and amenability / arXiv:1709:07287
Y. Ihara / 1966 / On discrete subgroups of the two by two projective linear group over p-adic elds / J. Math. Soc. Japan 18:219~235
H. Bass / 1993 / Covering theory for graphs of groups / J. Pure Appl. Algebra 89(1-2):3~47
H. Bass / 1990 / Uniform tree lattices / J. Amer. Math. Soc 3(4):843~902
R. Coulon / Growth gap in hyperbolic groups and amenability / arXiv:1709:07287
Y. Ihara / 1966 / On discrete subgroups of the two by two projective linear group over p-adic elds / J. Math. Soc. Japan 18:219~235
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