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

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]**Hirotada Anzai,*Ergodic skew product transformations on the torus*, Osaka Math. J.**3**(1951), 83–99. MR**0040594****[BMM]**Lawrence W. Baggett, Herbert A. Medina, and Kathy D. Merrill,*On functions that are trivial cocycles for a set of irrationals. II*, Proc. Amer. Math. Soc.**124**(1996), no. 1, 89–93. MR**1285971**, 10.1090/S0002-9939-96-02990-5**[BM]**Larry Baggett and Kathy Merrill,*Representations of the Mautner group and cocycles of an irrational rotation*, Michigan Math. J.**33**(1986), no. 2, 221–229. MR**837580**, 10.1307/mmj/1029003351**[GLL]**Patrick Gabriel, Mariusz Lemańczyk, and Pierre Liardet,*Ensemble d’invariants pour les produits croisés de Anzai*, Mém. Soc. Math. France (N.S.)**47**(1991), 102 (French, with English summary). MR**1125743****[HW]**G. H. Hardy and E. M. Wright,*An introduction to the theory of numbers*, 5th ed., The Clarendon Press, Oxford University Press, New York, 1979. MR**568909****[Med]**Herbert A. Medina,*Spectral types of unitary operators arising from irrational rotations on the circle group*, Michigan Math. J.**41**(1994), no. 1, 39–49. MR**1260607**, 10.1307/mmj/1029004913**[Mer]**Kathy D. Merrill,*Cohomology of step functions under irrational rotations*, Israel J. Math.**52**(1985), no. 4, 320–340. MR**829362**, 10.1007/BF02774084**[P]**Karl Petersen,*On a series of cosecants related to a problem in ergodic theory*, Compositio Math.**26**(1973), 313–317. MR**0325927****[R]**Arlan Ramsay,*Nontransitive quasi-orbits in Mackey’s analysis of group extensions*, Acta Math.**137**(1976), no. 1, 17–48. MR**0460531****[V]**William A. Veech,*Strict ergodicity in zero dimensional dynamical systems and the Kronecker-Weyl theorem 𝑚𝑜𝑑2*, Trans. Amer. Math. Soc.**140**(1969), 1–33. MR**0240056**, 10.1090/S0002-9947-1969-0240056-X

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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