• DOI:10.1090/S0002-9947-2014-06347-2
Corpus ID: 119115741

Fixed-point-free elements of iterated monodromy groups

@article{Jones2012FixedpointfreeEO,
  title={Fixed-point-free elements of iterated monodromy groups},
  author={R. Jones},
  journal={Transactions of the American Mathematical Society},
  year={2012},
  volume={367},
  pages={2023-2049}
}

R. Jones

Published 2012

Mathematics

Transactions of the American Mathematical Society

The iterated monodromy group of a post-critically finite complex polynomial of degree d \geq 2 acts naturally on the complete d-ary rooted tree T of preimages of a generic point. This group, as well as its pro-finite completion, act on the boundary of T, which is given by extending the branches to their "ends" at infinity. We show that for nearly all polynomials, elements that have fixed points on the boundary are rare, in that they belong to a set of Haar measure zero. The exceptions are those… CONTINUE READING

View PDF on arXiv

Save to Library

Create Alert

Cite

Launch Research Feed