Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Smooth actions of $R^n$


Author: Sol Schwartzman
Journal: Proc. Amer. Math. Soc. 134 (2006), 379-384
MSC (2000): Primary 37A15, 37C40
DOI: https://doi.org/10.1090/S0002-9939-05-08195-5
Published electronically: September 21, 2005
MathSciNet review: 2176005
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Given a smooth action of $R^n$ on a $k$-dimensional differentiable manifold $M^k$, for each $0\le r\le k$ we associate with ``almost all" oriented orbits of dimension $r$ an element of $H_r(M^k,R)$.


References [Enhancements On Off] (What's this?)

  • 1. N. Dunford, and J. Schwartz, Linear Operators - Part 1, Interscience publishers, (1958). MR 0117523 (22:8302)
  • 2. J. Kelley, General Topology, D. Van Nostrand, (1955). MR 0070144 (16:1136c)
  • 3. J.C. Oxtoby, Ergodic Sets, Bull. Amer. Math. Soc., 58(1952), 116-136. MR 0047262 (13:850e)
  • 4. S. Schwartzman, Asymptotic Cycles, Annals of Mathematics, Vol.66 no. 2, (1957). MR 0088720 (19:568i)
  • 5. S. Schwartzman, Higher Dimensional Asymptotic Cycles, Canadian Journal of Mathematics, Volume 55(3), (2003), 636-648 MR 1980617 (2004d:57036)
  • 6. D. Sullivan, Cycles for the Dynamical Study of Foliated Manifolds and Complex Manifolds, Inventiones Mathematica, 36(1976), 225-255. MR 0433464 (55:6440)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 37A15, 37C40

Retrieve articles in all journals with MSC (2000): 37A15, 37C40


Additional Information

Sol Schwartzman
Affiliation: Department of Mathematics, University of Rhode Island, Kingston, Rhode Island 02881

DOI: https://doi.org/10.1090/S0002-9939-05-08195-5
Received by editor(s): March 15, 2004
Published electronically: September 21, 2005
Communicated by: Michael Handel
Article copyright: © Copyright 2005 American Mathematical Society

American Mathematical Society