• Title/Summary/Keyword: Fibrations

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GENERALIZED GOTTLIEB SUBGROUPS AND SERRE FIBRATIONS

  • Kim, Jae-Ryong
    • Bulletin of the Korean Mathematical Society
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    • v.46 no.1
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    • pp.25-33
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    • 2009

  • Let ${\pi}:E{\rightarrow}B$ be a Serre fibration with fibre F. We prove that if the inclusion map $i:F{\rightarrow}E$ has a left homotopy inverse r and ${\pi}:E{\rightarrow}B$ admits a cross section ${\rho}:B{\rightarrow}E$, then $G_n(E,F){\cong}{\pi}_n(B){\oplus}G_n(F)$. This is a generalization of the case of trivial fibration which has been proved by Lee and Woo in [8]. Using this result, we will prove that ${\pi}_n(X^A){\cong}{\pi}_n(X){\oplus}G_n(F)$ for the function space $X^A$ from a space A to a weak $H_*$-space X where the evaluation map ${\omega}:X^A{\rightarrow}X$ is regarded as a fibration.

  • https://doi.org/10.4134/BKMS.2009.46.1.025 인용 PDF KSCI

ON EXTREMAL ELLIPTIC K3 SURFACES

  • Ye, Qiang
    • Journal of the Korean Mathematical Society
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    • v.36 no.6
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    • pp.1091-1113
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    • 1999

  • In this paper, we first classify the possible configurations of fibrations which are not semi-stable on extremal elliptic K3 surfaces. Then we give a complete list of extremal elliptic K3 surfaces whose singular fibers are all not of type $I_n$.

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