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4 results

  • A unified formula for Steenrod operations in flag manifolds

  • Haibao Duan, Xuezhi Zhao
  • Journal:
    Compositio Mathematica / Volume 143 / Issue 1 / January 2007
    Published online by Cambridge University Press:
    19 January 2007, pp. 257-270
    Print publication:
    January 2007
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  • The classical Schubert cells on a flag manifold $G/P$ give a cell decomposition for $G/P$ whose Kronecker duals (known as Schubert classes) form an additive base for the integral cohomology $H^{\ast}(G/P)$. We present a formula that expresses Steenrod mod-$p$ operations on Schubert classes in $G/P$ in terms of Cartan numbers of $G$.

  • Self-maps of the Grassmannian of Complex Structures Dedicated to Professor Boju Jiang on his 65th birthday

  • Haibao Duan
  • Journal:
    Compositio Mathematica / Volume 132 / Issue 2 / June 2002
    Published online by Cambridge University Press:
    04 December 2007, pp. 159-175
    Print publication:
    June 2002
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  • Let CSn be the flag manifold SO(2n)/U(n). We give a partial classification for the endomorphisms of the cohomology ring H*(CSn; Z) which is very close to a homotopy classification of all selfmaps of CSn. Applications concerning the geometry of the space are discussed.