Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
권호 표지

THE LEAST NUMBER OF COINCIDENCES WITH A COVERING MAP OF A POLYHEDRON

  • Published : 1999.09.01
Download PDF
⟨ Previous Next ⟩

Abstract

We define the coincidence index of pairs of maps p, f : $\widetilde{X}$ $\rightarrow$ X where p is a covering of a polyhedron X. We use a polyhedral transversality Theorem due to T. Plavchak. When p=identity we get the classical fixed point index of self map of polyhedra without using homology.

Keywords

References

  1. The Lefshetz Fixed Point Theorem R. F. Brown
  2. Rocky Mountain J. Math. v.23 The coincidence Nielsen theory on non-orientable manifolds R. Dobrenko;J. Jezierski
  3. Fund. Math. v.134 On the generalization of the Nielsen number R. Dobrenko;Z. Kuchariski
  4. Lectures on Algebraic Topology A. Dold
  5. London Math. Soc. Lecture Notes Ser. v.93 A geometrical approach to degree theory and the Leray-Schauder index J. Dugundji
  6. Lecture Notex in Math. 886;Fixed Point Theory 73-102 A simplicial approach to the fixed point index G. Fournier
  7. Fund. Math. v.153 Lefschetz coincidence formula on non-orientable manifolds D. l. Goncalves;J. Jezierski
  8. Math. Z. v.29 Uber die algebraische Anzahl Mindestzahlen von Fixpunkten H. Hopf
  9. Fund. Math. v.143 The Nielsen coincidence theory on topological manifolds J. Jezierski
  10. Contemp. Math. Amer. Math. Soc. v.14 Lectures on the Nielsen Fixed Point Theory B. J. Jiang
  11. American J. Math. v.102 The least number of fixed points B. J. Jiang
  12. Charlottesville Topology from the Differential Viewpoint J. Milnor
  13. Pacific J. Math. v.178 no.1 A polyhedral transversality theorem for one-parameter fixed point theory T. Plavchak
  14. Introduction to Piecewise Linear Topology Rourke, B. Sanderson
  15. J. Reine Angew. Math. v.194 Mindestzahlen von Koinzidenzpunkten H. Schirmer
  16. Algebraic Topology E. Spanier
  17. Homology Theory J. Vick