NIELSEN TYPE NUMBERS FOR PERIODIC POINTS ON THE COMPLEMENT

  • LIM, IN TAIK (Dept. of Mathematices, Chosun University Chosun University)
  • Received : 2002.05.01
  • Published : 2002.07.30

Abstract

A Nielsen number $\bar{N}(f:X-A)$ is a homotopy invariant lower bound for the number of fixed points on X-A where X is a compact connected polyhedron and A is a connected subpolyhedron of X. This number is extended to Nielsen type numbers $\bar{NP_{n}}(f:X-A)$ of least period n and $\bar{N{\phi}_{n}}(f:X-A)$ of the nth iterate on X-A where the subpolyhedron A of a compact connected polyhedron X is no longer path connected.

Keywords

periodic point;Nielsen type number

Acknowledgement

Supported by : chosun University

References

  1. Pacific J. of Math. v.117 Product formulae for Nielsen numbers of fibre maps Heath, P.R.
  2. Topological Fixed Point Theory and Applications, Proceedings, Tianjin 1988, Lecture Notes in Mathematics v.1411 Nielsen-type numbers for periodic points I Heath, P.R.;Piccinini, R.;You, C.
  3. Topology and its Appl. v.63 Nielsen type numbers for periodic points on nonconnected spaces Heath, P.R.;Schirmer, H.;You, C.
  4. Topology and its Appl. v.63 Nielsen type numbers for peridodic points on pairs of spaces Heath, P.R.
  5. Topology and its Appl. v.43 Nielsen-type numbers for periodic points II Heath, P.R.;You, C.
  6. Contemporary Math. v.14 Lectures on Nielsen Fixed Point Theory Jiang, B.
  7. Basic Science and Engineering v.1 A relative Nielsen number and all extension Nielsen number Lim, I.T.
  8. Pacific J. of Math. v.122 A Relative Nielsen number Schirmer, H.