• Title, Summary, Keyword: homotopy fixed point set

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HOMOTOPY FIXED POINT SET OF THE HOMOTOPY FIBRE

  • Lee, Hyang-Sook
    • Bulletin of the Korean Mathematical Society
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    • v.36 no.4
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    • pp.755-762
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    • 1999
  • Let X be a p-compace groyp, Y -> X bd a p-compact-subgroup of X and G -> X be a p-compact toral subgroup of X with $(X/Y)^{hG} \neq 0$. In this paper we show that the homotopy fixed point set of the homotopy fibre $(X/Y)^{hG}$ is $F_p$-finite.

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HOMOTOPY FIXED POINT SET $FOR \rho-COMPACT$ TORAL GROUP

  • Lee, Hyang-Sook
    • Bulletin of the Korean Mathematical Society
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    • v.38 no.1
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    • pp.143-148
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    • 2001
  • First, we show the finiteness property of the homotopy fixed point set of p-discrete toral group. Let $G_\infty$ be a p-discrete toral group and X be a finite complex with an action of $G_\infty such that X^K$ is nilpotent for each finit p-subgroup K of $G_\infty$. Assume X is $F_\rho-complete$. Then X(sup)hG$\infty$ is F(sub)p-finite. Using this result, we give the condition so that X$^{hG}$ is $F_\rho-finite for \rho-compact$ toral group G.

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FIXED POINTS AND HOMOTOPY RESULTS FOR ĆIRIĆ-TYPE MULTIVALUED OPERATORS ON A SET WITH TWO METRICS

  • Lazar, Tania;O'Regan, Donal;Petrusel, Adrian
    • Bulletin of the Korean Mathematical Society
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    • v.45 no.1
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    • pp.67-73
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    • 2008
  • The purpose of this paper is to present some fixed point results for nonself multivalued operators on a set with two metrics. In addition, a homotopy result for multivalued operators on a set with two metrics is given. The data dependence and the well-posedness of the fixed point problem are also discussed.

ISOTROPY REPRESENTATIONS OF CYCLIC GROUP ACTIONS ON HOMOTOPY SPHERES

  • Suh, Dong-Youp
    • Bulletin of the Korean Mathematical Society
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    • v.25 no.2
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    • pp.175-178
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    • 1988
  • Let .SIGMA. be a smooth compact manifold without boundary having the same homotopy type as a sphere, which is called a homotopy sphere. Supose a group G acts smoothly on .SIGMA. with the fixed point set .SIGMA.$^{G}$ consists of two isolated fixed points p and q. In this case, tangent spaces $T_{p}$ .SIGMA. and $T_{q}$ .SIGMA. at isolated fixed points, as isotropy representations of G are called Smith equivalent. Moreover .SIGMA. is called a supporting homotopy sphere of Smith equivalent representations $T_{p}$ .SIGMA. and $T_{q}$ .SIGMA.. The study on Smith equivalence has rich history, and for this we refer the reader to [P] or [Su]. The following question of pp.A.Smith [S] motivates the study on Smith equivalence.e.

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