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The projective fundamental group of a Z(2)-shift
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UNSPECIFIED (1995) The projective fundamental group of a Z(2)-shift. ERGODIC THEORY AND DYNAMICAL SYSTEMS, 15 (Part 6). pp. 1091-1118. ISSN 0143-3857.
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Abstract
We define a new invariant for symbolic Z(2)-actions, the projective fundamental group. This invariant is the limit of an inverse system of groups, each of which is the fundamental group of a space associated with the Z(2)-action. The limit group measures a kind of long-distance order that is manifested along loops in the plane, and roughly speaking bears the same relation to the mixing properties of the Z(2)-action that pi(1) of a topological space bears to pi(0). The projective fundamental group is invariant under topological conjugacy. We calculate this invariant for several important examples of Z(2)-actions, and use it to prove non-existence of certain constant to-one factor maps between two-dimensional subshifts. Subshifts that have the same entropy and periodic point data can have different projective fundamental groups.
Item Type: | Journal Article | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Journal or Publication Title: | ERGODIC THEORY AND DYNAMICAL SYSTEMS | ||||
Publisher: | CAMBRIDGE UNIV PRESS | ||||
ISSN: | 0143-3857 | ||||
Official Date: | December 1995 | ||||
Dates: |
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Volume: | 15 | ||||
Number: | Part 6 | ||||
Number of Pages: | 28 | ||||
Page Range: | pp. 1091-1118 | ||||
Publication Status: | Published |
Data sourced from Thomson Reuters' Web of Knowledge
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