A Classification of Smooth Embeddings of 4-manifolds in 7-space, Ii
نویسندگان
چکیده
Let N be a closed, connected, smooth 4-manifold with H1(N ;Z) = 0. Our main result is the following classification of the set E(N) of smooth embeddings N → R up to smooth isotopy. Haefliger proved that the set E(S) with the connected sum operation is a group isomorphic to Z12. This group acts on E(N) by embedded connected sum. Boéchat and Haefliger constructed an invariant BH : E(N) → H2(N ;Z) which is injective on the orbit space of this action; they also described im(BH). We determine the orbits of the action: for u ∈ im(BH) the number of elements in BH(u) is GCD(u/2, 12) if u is divisible by 2, or is GCD(u, 3) if u is not divisible by 2. The proof is based on a new approach using modified surgery as developed by Kreck.
منابع مشابه
A Classification of Smooth Embeddings of 4-manifolds in 7-space, I
We work in the smooth category. Let N be a closed connected n-manifold and assume that m > n + 2. Denote by E(N) the set of embeddings N → R up to isotopy. The group E(S) acts on E(N) by embedded connected summation of a manifold and a sphere. If E(S) is non-zero (which often happens for 2m < 3n + 4) then until recently no results on this action and no complete description of E(N) were known. O...
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