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- W2000675483 abstract "Let $M$ be a compact, orientable, $k$-dimensional real differentiaable manifold and $N$ an $n$-dimensional complex manifold, where $k geq n$. Given an immersion $iota :M to N$, a point $x in M$ is called an RC-singular point of the immersion if the tangent space to $iota (M)$ at $iota (x)$ contains a complex subspace of dimension $> k - n$. This paper is devoted to the study of the cohomological properties of the set of RC-singular points of an immersion. When $k = 2n - 2$, the following formula is obtained: [ Omega (M) + sum limits _{r = 0}^{n - 1} {tilde Omega } {(iota )^{n - r - 1}}{iota ^ ast }{c_r}(N) = 2{t^ ast }DK,] where $Omega (M)$ is the Euler class of $M,widetilde Omega (iota )$ is the Euler class of the normal bundle of the immersion, ${c_r}(N)$ are the Chern classes of $N$, and ${t^ ast }DK$ is a cohomology class of degree $2n - 2$ in $M$ whose value on the fundamental class of $M$ gives the algebraic number of RC-singular points of $iota$. Various applications are discussed. For $n leq k leq 2n - 2$, it is shown that, as long as dimensions allow, all Pontrjagin classes and the Euler class of $M$ are carried by subsets of the set of RC-singularities of an immersion $iota :M to {{text {C}}^n}$." @default.
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- W2000675483 date "1972-01-01" @default.
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- W2000675483 title "Characteristic classes of real manifolds immersed in complex manifolds" @default.
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- W2000675483 doi "https://doi.org/10.1090/s0002-9947-1972-0314066-8" @default.
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