About the Chern class of infinite complex Grassmannian
$begingroup$
I learned that any characteristic class of rank-$k$ complex vector bundles on paracompact spaces is determined bijectively by a cohomology class in $H^*(Gr_k^infty(mathbb C))$, the cohomology ring of k-th infinite Grassmannian.
So the $n$-th Chern classes should be able to defined just by an element of $H^{2n}(Gr_k^infty(mathbb C))$, which is a linear combination of certain Schubert cycles (or Young diagrams, equivalently). Is there a direct combinatorial way to define what the Chern classes are?
algebraic-geometry algebraic-topology complex-geometry schubert-calculus
edited Jan 5 at 12:38
Matt Samuel
38.7k63769
asked Aug 7 '14 at 1:59
Y.H.Y.H.
503212
$endgroup$
add a comment |
$begingroup$
I learned that any characteristic class of rank-$k$ complex vector bundles on paracompact spaces is determined bijectively by a cohomology class in $H^*(Gr_k^infty(mathbb C))$, the cohomology ring of k-th infinite Grassmannian.
So the $n$-th Chern classes should be able to defined just by an element of $H^{2n}(Gr_k^infty(mathbb C))$, which is a linear combination of certain Schubert cycles (or Young diagrams, equivalently). Is there a direct combinatorial way to define what the Chern classes are?
algebraic-geometry algebraic-topology complex-geometry schubert-calculus
edited Jan 5 at 12:38
Matt Samuel
38.7k63769
asked Aug 7 '14 at 1:59
Y.H.Y.H.
503212
$endgroup$
add a comment |
$begingroup$
I learned that any characteristic class of rank-$k$ complex vector bundles on paracompact spaces is determined bijectively by a cohomology class in $H^*(Gr_k^infty(mathbb C))$, the cohomology ring of k-th infinite Grassmannian.
So the $n$-th Chern classes should be able to defined just by an element of $H^{2n}(Gr_k^infty(mathbb C))$, which is a linear combination of certain Schubert cycles (or Young diagrams, equivalently). Is there a direct combinatorial way to define what the Chern classes are?
algebraic-geometry algebraic-topology complex-geometry schubert-calculus
edited Jan 5 at 12:38
Matt Samuel
38.7k63769
asked Aug 7 '14 at 1:59
Y.H.Y.H.
503212
$endgroup$
I learned that any characteristic class of rank-$k$ complex vector bundles on paracompact spaces is determined bijectively by a cohomology class in $H^*(Gr_k^infty(mathbb C))$, the cohomology ring of k-th infinite Grassmannian.
So the $n$-th Chern classes should be able to defined just by an element of $H^{2n}(Gr_k^infty(mathbb C))$, which is a linear combination of certain Schubert cycles (or Young diagrams, equivalently). Is there a direct combinatorial way to define what the Chern classes are?
algebraic-geometry algebraic-topology complex-geometry schubert-calculus
algebraic-geometry algebraic-topology complex-geometry schubert-calculus
edited Jan 5 at 12:38
Matt Samuel
38.7k63769
asked Aug 7 '14 at 1:59
Y.H.Y.H.
503212
edited Jan 5 at 12:38
Matt Samuel
38.7k63769
asked Aug 7 '14 at 1:59
Y.H.Y.H.
503212
edited Jan 5 at 12:38
Matt Samuel
38.7k63769
edited Jan 5 at 12:38
Matt Samuel
38.7k63769
edited Jan 5 at 12:38
Matt Samuel
38.7k63769
38.7k63769
asked Aug 7 '14 at 1:59
Y.H.Y.H.
503212
asked Aug 7 '14 at 1:59
Y.H.Y.H.
503212
asked Aug 7 '14 at 1:59
Y.H.Y.H.
503212
503212
add a comment |
add a comment |
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