Generic immersions and totally real embeddings

Naohiko Kasuya; Masamichi Takase

doi:10.1142/s0129167x18500738

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arXiv · 1803.08238

Generic immersions and totally real embeddings

Naohiko Kasuya·Masamichi Takase

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Abstract

We show that, for a closed orientable n-manifold, with n not congruent to 3 modulo 4, the existence of a CR-regular embedding into complex (n-1)-space ensures the existence of a totally real embedding into complex n-space. This implies that a closed orientable (4k+1)-manifold with non-vanishing Kervaire semi-characteristic possesses no CR-regular embedding into complex 4k-space. We also pay special attention to the cases of CR-regular embeddings of spheres and of simply-connected 5-manifolds.

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Naohiko Kasuya, Masamichi Takase. 2018-03-22. Generic immersions and totally real embeddings. https://doi.org/10.1142/s0129167x18500738

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