The Arf-Kervaire invariant of framed manifolds as an obstruction to embeddability - Mathematics > Algebraic TopologyReport as inadecuate




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Abstract: We define a quadratic form which gives an obstruction to embedding $N^{4k+2}\subset \R^{6k+4}$ of a smooth highly connected manifold into Euclidean space,with sufficiently many nondegenerate sections of the normal bundle. As the maincorollary we prove that no 14-connected resp. 30-connected stablyparallelizable manifold $N^{30}$ resp. $N^{62}$ with Arf-Kervaire invariantone is smoothly embeddable into $\R^{36}$ resp. $\R^{83}$.



Author: Peter M. Akhmetiev, Matija Cencelj, Dušan Repovš

Source: https://arxiv.org/







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