Equivariant method for periodic maps
HTML articles powered by AMS MathViewer
- by Wu Hsiung Huang
- Trans. Amer. Math. Soc. 189 (1974), 175-183
- DOI: https://doi.org/10.1090/S0002-9947-1974-0334247-9
- PDF | Request permission
Abstract:
The notion of coherency with submanifolds for a Morse function on a manifold is introduced and discussed in a general way. A Morse inequality for a given periodic transformation which compares the invariants called qth Euler numbers on fixed point set and the invariants called qth Lefschetz numbers of the transformations is thus obtained. This gives a fixed point theorem in terms of qth Lefschetz number for arbitrary q.References
- Shiing-shen Chern, A simple intrinsic proof of the Gauss-Bonnet formula for closed Riemannian manifolds, Ann. of Math. (2) 45 (1944), 747–752. MR 11027, DOI 10.2307/1969302
- Shoshichi Kobayashi, Fixed points of isometries, Nagoya Math. J. 13 (1958), 63–68. MR 103508, DOI 10.1017/S0027763000023497
- J. Milnor, Morse theory, Annals of Mathematics Studies, No. 51, Princeton University Press, Princeton, N.J., 1963. Based on lecture notes by M. Spivak and R. Wells. MR 0163331, DOI 10.1515/9781400881802
- Marston Morse, The calculus of variations in the large, American Mathematical Society Colloquium Publications, vol. 18, American Mathematical Society, Providence, RI, 1996. Reprint of the 1932 original. MR 1451874, DOI 10.1090/coll/018
- Robert Hermann, Differential geometry and the calculus of variations, Mathematics in Science and Engineering, Vol. 49, Academic Press, New York-London, 1968. MR 0233313
Bibliographic Information
- © Copyright 1974 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 189 (1974), 175-183
- MSC: Primary 57D70
- DOI: https://doi.org/10.1090/S0002-9947-1974-0334247-9
- MathSciNet review: 0334247