A new invariant and parametric connected sum of embeddings

• Autorzy: A. Skopenkov
• Języki publikacji: 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.

Kategorie tematyczne

• 57Q35: Embeddings and immersions
• 55S15: Symmetric products, cyclic products
• 55Q91: Equivariant homotopy groups
• 57R40: Embeddings
• 57Q37: Isotopy

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2007
• Tom: 197
• Numer: 1
• Strony: 253-269

Daty

wydano

2007

Twórcy

autor

A. Skopenkov

• 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

Identyfikatory

DOI

10.4064/fm197-0-12