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Cohomology of polynomials under an irrational rotation
Author(s):
Lawrence
W.
Baggett;
Herbert
A.
Medina;
Kathy
D.
Merrill
Journal:
Proc. Amer. Math. Soc.
126
(1998),
2909-2918.
MSC (1991):
Primary 28D05, 11K38
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Abstract:
A new description of cohomology of functions under an irrational rotation is given in terms of symmetry properties of the functions on subintervals of ![$[0,1].$](/proc/1998-126-10/S0002-9939-98-04424-4/gif-abstract/img1.gif) This description yields a method for passing information about the cohomology classes for a given irrational to the cohomology classes for an equivalent irrational.
References:
- [A]
- H. Anzai, Ergodic skew product transformations on the torus, Osaka J. Math. 3 (1951), 83-99. MR 12:719d
- [BMM]
- L. Baggett, H. A. Medina, and K. D. Merrill, On functions that are trivial cocycles for a set of irrationals, II, Proc. Amer. Math. Soc. 124 (1996), 89-93. MR 96d:28014
- [BM]
- L. Baggett and K. D. Merrill, Representations of the Mautner group and cocycles of an irrational rotation, Michigan Math. J. 33 (1986), 221-229. MR 87h:22011
- [GLL]
- P. Gabriel, M. Lema\'{n}czyk, and P. Liardet, Ensemble d'invariants pour les produits croisés de Anzai, Mémoire SMF no. 47 119(3) ( 1991). MR 93b:28042
- [HW]
- G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers, Oxford University Press, 1962. MR 81i:10002
- [Med]
- H. A. Medina, Spectral Types of Unitary Operators Arising from Irrational Rotations on the Circle Group, Michigan Math. J. 41(1) (1994), 39-49. MR 95a:28014
- [Mer]
- K. D. Merrill, Cohomology of step functions under irrational rotations, Israel J. Math 52 (1985), 320-340. MR 88b:39009
- [P]
- K. Petersen, On a series of cosecants related to a problem in ergodic theory, Compos. Math. 26 ( 1973), 313-317. MR 48:4273
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- A. Ramsay, Nontransitive quasiorbits in Mackey's analysis of group extensions, Acta Math. 137 ( 1976), 17-48. MR 57:524
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- W. A. Veech, Strict ergodicity in zero-dimensional dynamical systems and the Kronecker-Weyl theorem mod 2, Trans. Am. Math. Soc. 140 ( 1969), 1-33. MR 39:1410
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Additional Information:
Lawrence
W.
Baggett
Affiliation:
Department of Mathematics, University of Colorado, Boulder, Colorado 80309
Email:
baggett@euclid.colorado.edu
Herbert
A.
Medina
Affiliation:
Department of Mathematics, Loyola Marymount University, Los Angeles, California 90045
Email:
hmedina@lmumail.lmu.edu
Kathy
D.
Merrill
Affiliation:
Department of Mathematics, The Colorado College, Colorado Springs, Colorado 80903
Email:
kmerrill@cc.colorado.edu
DOI:
10.1090/S0002-9939-98-04424-4
PII:
S 0002-9939(98)04424-4
Received by editor(s):
February 26, 1997
Additional Notes:
This research was partially supported by NSF grants DMS9201720 and DMS9401180.
Communicated by:
David R. Larson
Copyright of article:
Copyright
1998,
American Mathematical Society
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