대한수학회논문집 (Communications of the Korean Mathematical Society)

  • 제15권2호
  • /
  • Pages.349-355
  • /
  • 2000
  • /
  • 1225-1763(pISSN)
  • /
  • 2234-3024(eISSN)
대한수학회 (Korean Mathematical Society)
권호 표지

On Homotopy Equivalence Of Nonnilpotent Spaces And Its Applications

  • Han, Sang-eon (Department of Mathematics College of Natural Science Honam University)
  • 발행 : 2000.04.01
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초록

In this paper we generalize the Whitehead theorem which says that a homology equivalence implies a homotopy equivalence for nilpotent spaces. We make some theorems on a homotopy equivalence of non-nilpotent spaces, e.g., the solvable space or space satisfying the condition (T**) or space X with $\pi$1(X) Engel, or locally nilpotent space with some properties. Furthermore we find some conditions that the Wall invariant will be trivial.

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참고문헌

  1. L. N. S v.304 Homotopy Limits, Completions and Localization A. K. Bousfield;D. M. Kan
  2. L. N. M v.249 A generalization of the Whitehead theorem E. Dror
  3. Proc. of A. M. S v.47 no.1 The Whitechead theorem for nilpotent spaces S. M. Gersten
  4. Tamkang Jour. of Math v.29 no.2 On the Euler characteristic of the space satisfying condition (T**) Sang-Eon Han
  5. Kyushu J. Math v.52 no.2 On the R-good property of the space satisfying condition(T**) Sang-Eon Han
  6. Topology and its applications On the space satisfying conditions (T*) or (T**) and its applications II Sang-Eon Han
  7. Tsukuba J. of Math v.22 no.1 Wall invariant for the space satisfying the condition(T**) Sang-Eon Han
  8. Quart. J. Math. Oxford v.27 On the Zeeman comparison theorem for the homology of quasi-nilpotent fibrations P. J. Hilton;J. Roiterberg
  9. Topolgy v.14 Wall obstruction of the nilpotent spaces G. Mislin
  10. A Courses in the Theory of Groups D. J. S. Robinson
  11. Glasgow Math. J v.39 Groups with few nonnilpotent subgroups H. Smith