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A minimum fixed point theorem for smooth fiber preserving maps
Author(s):
Catherine
Lee
Journal:
Proc. Amer. Math. Soc.
135
(2007),
1547-1549.
MSC (2000):
Primary 55M20, 55R10, 58A05
Posted:
November 15, 2006
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Abstract:
Let  be a smooth fiber bundle. Given a smooth fiber preserving map  , we will show that  can be deformed by a smooth, fiber preserving homotopy to a smooth map  such that the number of fixed points of  is equal to the fiberwise Nielsen number of  .
References:
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- 1.
- R.F. Brown, On a homotopy converse to the Lefschetz fixed point theorem, Pacific J. Math. 17 (1966), 407-411. MR 0195083 (33:3288)
- 2.
- B.A. Dubrovin, A.T. Fomenko, and S.P. Novikov, Modern geometry--methods and applications. Part II, Graduate Texts in Mathematics, vol. 104, Springer-Verlag, New York, 1985, Translated from the Russian by Robert G. Burns.MR 0807945 (86m:53001)
- 3.
- P. Heath, E. Keppelmann, and P. Wong, Addition formulae for Nielsen numbers and for Nielsen type numbers of fibre preserving maps, Topology Appl. 67 (1995).MR 1362079 (96m:55003)
- 4.
- B.-J. Jiang, Fixed point classes from a differential viewpoint, Fixed point theory (Sherbrooke, Que., 1980), Lecture Notes in Math., vol. 886, Springer, Berlin, 1981, pp. 163-170.MR 0643005 (83a:55003)
- 5.
- C. Lee, The affect of smoothness and derivative conditions on the fixed point sets of smooth maps, Ph.D. Thesis, University of California, Los Angeles, December, 2005.
- 6.
- F. Wecken, Fixpunktklassen. III. Mindestzahlen von Fixpunkten, Math. Ann. 118 (1942), 544-577. MR 0010281 (5:275b)
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Additional Information:
Catherine
Lee
Affiliation:
Department of Mathematics, University of California, Los Angeles, California 90095-1555
Address at time of publication:
1111 Laveta Terrace, Los Angeles, California 90026
Email:
cathylee@math.ucla.edu
DOI:
10.1090/S0002-9939-06-08600-X
PII:
S 0002-9939(06)08600-X
Received by editor(s):
July 7, 2005
Received by editor(s) in revised form:
December 2, 2005
Posted:
November 15, 2006
Additional Notes:
This paper is based on a part of the author's Ph.D. dissertation written under the supervision of Robert F. Brown.
Dedicated:
This paper is dedicated to my advisor, Robert F. Brown
Communicated by:
Paul Goerss
Copyright of article:
Copyright
2006,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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