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# All Questions

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### Generalizing the formula between Wu class and the Steenrod square

I know that on the tangent bundle of $M^d$, the corresponding Wu class and the Steenrod square satisfy $$Sq^{d-j}(x_j)=u_{d-j} x_j, \text{ for any } x_j \in H^j(M^d;\mathbb Z_2) . \tag{eq.1}$$ ...
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### Generalized Postnikov square

Following Wikipedia (https://en.wikipedia.org/wiki/Postnikov_square), a Postnikov square is a certain cohomology operation from a first cohomology group $H^1$ to a third cohomology group $H^3$, ...
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Let $(E^{\cdot},d_E^{\cdot})$ be a cochain complex of complex vector bundles on a smooth compact manifold $X$. Now for each $E^i$ we could assign a connection $\nabla_E^i$ and obtain its curvature $(\... 0answers 141 views ### Cohomology classes functorial under etale morphisms Consider the full subcategory$\mathcal C$in the big etale site of a field$k$consisting of smooth schemes, namely the category of smooth varieties over a field$k$with etale maps as morphisms. I ... 0answers 724 views ### Local proof of Grothendieck-Riemann-Roch theorem There is a theorem by Feigin and Tsygan(Theorem 1.3.3 here) which they call "Riemann-Roch" theorem. Given a smooth morphism$f:S\to N$of relative dimension$n$and a vector bundle$E/S$of rank$k\$ ...

山西福彩快乐十分钟

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