Stable almost complex structures on certain $10$-manifolds

Huijun Yang

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arXiv · 1808.04534

Stable almost complex structures on certain $10$-manifolds

Huijun Yang

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Abstract

Let $M$ be a $10$-dimensional closed oriented smooth manifold. Set $$\mathcal{D}_{M} := \{ x \in H^{2}(M; \Z/2) \mid x^{2} + w_{2}(M) x \in \rho_{2} ( TH^{4}(M;\Z) ) \}.$$ Suppose that $H_{1}(M;\Z)=0$ and $\mathcal{D}_{M} \subset \rho_{2}( H^{2}(M; \Z) )$. Then the necessary and sufficient conditions for $M$ to admit a stable almost complex structure are determined in terms of the characteristic classes and cohomology ring of $M$.

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BibTeX RIS

Huijun Yang. 2018-08-14. Stable almost complex structures on certain $10$-manifolds. https://arxiv.org/abs/1808.04534

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