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A parametrized fixed point theorem
Author(s):
Vesta
Coufal
Journal:
Proc. Amer. Math. Soc.
137
(2009),
3939-3942.
MSC (2000):
Primary 55M20, 57Rxx
Posted:
July 13, 2009
MathSciNet review:
2529904
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Abstract:
We use bordism theory to extend Lefschetz-Nielsen theory to a family of manifolds and endomorphisms. In particular, we define an invariant, and prove a parametrized fixed point theorem and its converse.
References:
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A Family Version of Lefschetz-Nielsen Fixed Point Theory.
Ph.D. thesis, University of Notre Dame, Notre Dame, Indiana, 2004. - 2.
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Generalized normal bundles for locally-flat imbeddings.
Trans. Amer. Math. Soc., 114:488-513, 1965. MR 0179795 (31:4037) - 3.
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Nielsen fixed point theory.
In Handbook of geometric topology, pages 499-521. North-Holland, Amsterdam, 2002. MR 1886677 (2003c:55003) - 4.
- Allen Hatcher and Frank Quinn.
Bordism invariants of intersections of submanifolds.
Trans. Amer. Math. Soc., 200:327-344, 1974. MR 0353322 (50:5806) - 5.
- John R. Klein and E. Bruce Williams.
Homotopical intersection theory. I.
Geom. Topol., 11:939-977, 2007. MR 2326939 (2008g:55011) - 6.
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The category of submersions.
Bull. Acad. Polon. Sci. Sér. Sci. Math., 27(3-4):321-326, 1979. MR 552057 (81a:57031)
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Additional Information:
Vesta
Coufal
Affiliation:
Department of Mathematics, Gonzaga University, Spokane, Washington 99258
Email:
coufal@gonzaga.edu
DOI:
10.1090/S0002-9939-09-09978-X
PII:
S 0002-9939(09)09978-X
Received by editor(s):
March 18, 2009
Posted:
July 13, 2009
Communicated by:
Brooke Shipley
Copyright of article:
Copyright
2009,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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