The chameleon groups of Richard J. Thompson: automorphisms and dynamics
نویسنده
چکیده
Part I. Background . . . . . . . . . . . . . . . . . . . . . . . . 1 0. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 1 1. Statements, history and outline . . . . . . . . . . . . . . . . . . 3 2. Transitivity properties of Thompson’s groups . . . . . . . . . . . . 10 Part II. Generalities . . . . . . . . . . . . . . . . . . . . . . 14 3. Germs, half germs, germ functions and germ generators . . . . . . . . 14 4. Normalizers and germs of Thompson’s groups . . . . . . . . . . . 22 5. Realizing automorphisms . . . . . . . . . . . . . . . . . . . 25 Part III. PL normalizers . . . . . . . . . . . . . . . . . . . . 28 6. Proof of Theorems 1 and 2 from Theorem 3 . . . . . . . . . . . . 28 Part IV. Non-PL normalizers — proof of Theorem 3 . . . . . . . . 32 7. Markov partitions . . . . . . . . . . . . . . . . . . . . . . 32 8. Trees . . . . . . . . . . . . . . . . . . . . . . . . . . 35 9. The calculus of break values . . . . . . . . . . . . . . . . . . 36 10. Criteria for piecewise linearity . . . . . . . . . . . . . . . . . 39 10.1. The piecewise linearity of h . . . . . . . . . . . . . . . . 39 10.2. The piecewise linearity of hνnh . . . . . . . . . . . . . . 43 11. Relating the criteria . . . . . . . . . . . . . . . . . . . . 45 11.1. Locating d . . . . . . . . . . . . . . . . . . . . . . 46 11.2. Verifying properties . . . . . . . . . . . . . . . . . . . 50 Part V. Examples . . . . . . . . . . . . . . . . . . . . . . . 52 12. Machinery . . . . . . . . . . . . . . . . . . . . . . . . 52 13. The examples . . . . . . . . . . . . . . . . . . . . . . . 55
منابع مشابه
Automorphisms of Generalized Thompson Groups
0.1. Results. We study the automorphisms of some generalizations of Thompson’s groups and their underlying structures. The automorphism groups of two of Thompson’s original groups were analyzed in [2] and were shown to be “small” and “unexotic.” Our results differ sharply from [2] in that we show that the automorphism groups of the generalizations are “large” and have “exotic” elements. The ter...
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