The Arf-Kervaire invariant of framed manifolds as an obstruction to embeddability

Details The Arf-Kervaire invariant of framed manifolds as an obstruction to embeddability The Arf-Kervaire invariant of framed manifolds as an obstruction to embeddability

2008-04-19

arxiv.org/abs/0804.3164v3

Mathematics

Algebraic Topology

Scientific paper

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 main corollary we prove that no 14-connected (resp. 30-connected) stably parallelizable manifold $N^{30}$ (resp. $N^{62}$) with Arf-Kervaire invariant one is smoothly embeddable into $\R^{36}$ (resp. $\R^{83}$).

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