Cohomology of polynomials

under an irrational rotation

Authors:
Lawrence W. Baggett, Herbert A. Medina and Kathy D. Merrill

Journal:
Proc. Amer. Math. Soc. **126** (1998), 2909-2918

MSC (1991):
Primary 28D05, 11K38

DOI:
https://doi.org/10.1090/S0002-9939-98-04424-4

MathSciNet review:
1459104

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Abstract | References | Similar Articles | Additional Information

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 This description yields a method for passing information about the cohomology classes for a given irrational to the cohomology classes for an equivalent irrational.

**[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****[R]**A. Ramsay,*Nontransitive quasiorbits in Mackey's analysis of group extensions*, Acta Math.**137**( 1976), 17-48. MR**57:524****[V]**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:
https://doi.org/10.1090/S0002-9939-98-04424-4

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

Article copyright:
© Copyright 1998
American Mathematical Society