Fixed Point Theory and Applications
Volume 2006 (2006), Article ID 17563, 10 pages
doi:10.1155/FPTA/2006/17563

Duan's fixed point theorem: Proof and generalization

Martin Arkowitz

Department of Mathematics, Dartmouth College, Hanover 03755, NH, USA

Received 25 July 2004; Revised 6 January 2005; Accepted 21 July 2005

Copyright © 2006 Martin Arkowitz. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. R. F. Brown, The Lefschetz Fixed Point Theorem, Scott, Foresman, Illinois, 1971.
  2. Y. Félix, S. Halperin, and J.-C. Thomas, Rational Homotopy Theory, vol. 205 of Graduate Texts in Mathematics, Springer, New York, 2001.
  3. P. A. Griffiths and J. W. Morgan, Rational Homotopy Theory and Differential Forms, vol. 16 of Progress in Mathematics, Birkhäuser, Massachusetts, 1981.
  4. D. Haibao, “A characteristic polynomial for self-maps of H-spaces,” The Quarterly Journal of Mathematics. Oxford. Second Series (2), vol. 44, no. 175, pp. 315–325, 1993.
  5. S. Halperin, “Spaces whose rational homology and de Rham homotopy are both finite-dimensional,” in Algebraic Homotopy and Local Algebra (Luminy, 1982), vol. 113-114 of Astérisque, pp. 198–205, Soc. Math. France, Paris, 1984.
  6. Y. Hemmi, K. Morisugi, and H. Ooshima, “Self maps of spaces,” Journal of the Mathematical Society of Japan, vol. 49, no. 3, pp. 438–453, 1997.
  7. T. Hungerford, Abstract Algebra: An Introduction, Saunders college, Pennsylvania, 1990.
  8. G. Lupton and J. Oprea, “Fixed points and powers of self-maps of H-spaces,” Proceedings of the American Mathematical Society, vol. 124, no. 10, pp. 3235–3239, 1996.
  9. J. W. Milnor and J. C. Moore, “On the structure of Hopf algebras,” Annals of Mathematics. Second Series (2), vol. 81, pp. 211–264, 1965.
  10. E. H. Spanier, Algebraic Topology, McGraw-Hill, New York, 1966.