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Group colorings and Bernoulli subflows / Su Gao, Steve Jackson and Brandon Seward.

By: Contributor(s): Material type: TextTextSeries: Memoirs of the American Mathematical Society ; v 241, no 1141.Publication details: Providence : American Mathematical Society, 2016.Description: vi, 241 pages : illustrations ; 26 cmISBN:
  • 9781470418472 (pbk. : acidfree paper)
Subject(s): DDC classification:
  • 510 23 Am512
Contents:
1. Introduction -- 2. Preliminaries -- 3. Basic constructions of 2-colorings -- 4. Marker structures and tilings -- 5. Blueprints and fundamental functions -- 6. Basic applications of the fundamental method -- 7. Further study of fundamental functions -- 8. The descriptive complexity of sets of 2-colorings -- 9. The complexity of the topological conjugacy relation -- 10. Extending partial functions to 2-colorings -- 11. Further questions.
Summary: In this paper the authors study the dynamics of Bernoulli flows and their subflows over general countable groups. One of the main themes of this paper is to establish the correspondence between the topological and the symbolic perspectives. From the topological perspective, the authors are particularly interested in free subflows (subflows in which every point has trivial stabilizer), minimal subflows, disjointness of subflows, and the problem of classifying subflows up to topological conjugacy. Their main tool to study free subflows will be the notion of hyper aperiodic points; a point is hyper aperiodic if the closure of its orbit is a free subflow.
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Holdings
Item type Current library Call number Status Date due Barcode Item holds
Books ISI Library, Kolkata 510 Am512 (Browse shelf(Opens below)) Available 137654
Total holds: 0

Includes bibliographical references and index.

1. Introduction --
2. Preliminaries --
3. Basic constructions of 2-colorings --
4. Marker structures and tilings --
5. Blueprints and fundamental functions --
6. Basic applications of the fundamental method --
7. Further study of fundamental functions --
8. The descriptive complexity of sets of 2-colorings --
9. The complexity of the topological conjugacy relation --
10. Extending partial functions to 2-colorings --
11. Further questions.

In this paper the authors study the dynamics of Bernoulli flows and their subflows over general countable groups. One of the main themes of this paper is to establish the correspondence between the topological and the symbolic perspectives. From the topological perspective, the authors are particularly interested in free subflows (subflows in which every point has trivial stabilizer), minimal subflows, disjointness of subflows, and the problem of classifying subflows up to topological conjugacy. Their main tool to study free subflows will be the notion of hyper aperiodic points; a point is hyper aperiodic if the closure of its orbit is a free subflow.

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