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• # Artykuł - szczegóły

## Fundamenta Mathematicae

2007 | 197 | 1 | 253-269

## A new invariant and parametric connected sum of embeddings

EN

### Abstrakty

EN
We define an isotopy invariant of embeddings $N → ℝ^{m}$ of manifolds into Euclidean space. This invariant together with the α-invariant of Haefliger-Wu is complete in the dimension range where the α-invariant could be incomplete. We also define parametric connected sum of certain embeddings (analogous to surgery). This allows us to obtain new completeness results for the α-invariant and the following estimation of isotopy classes of embeddings. In the piecewise-linear category, for a (3n-2m+2)-connected n-manifold N with (4n+5)/3 ≤ m ≤ (3n+2)/2, each preimage of the α-invariant injects into a quotient of $H_{3n-2m+3}(N)$, where the coefficients are ℤ for m-n odd and ℤ₂ for m-n even.

253-269

wydano
2007

### Twórcy

autor
• Department of Differential Geometry, Faculty of Mechanics and Mathematics, Moscow State University, Moscow 119992, Russia
• Independent University of Moscow, B. Vlasyevskiy, 11, Moscow 119002, Russia