77 research outputs found
A new invariant and parametric connected sum of embeddings
We define an isotopy invariant of embeddings N -> R^m of manifolds into
Euclidean space. This invariant together with the \alpha-invariant of
Haefliger-Wu is complete in the dimension range where the \alpha-invariant
could be incomplete. We also define parametric connected sum of certain
embeddings (analogous to surgery). This allows to obtain new completeness
results for the \alpha-invariant and the following estimation of isotopy
classes of embeddings.
For the piecewise-linear category, a (3n-2m+2)-connected n-manifold N and
(4n+4)/3 < m < (3n+3)/2 each preimage of \alpha-invariant injects into a
quotient of H_{3n-2m+3}(N), where the coefficients are Z for m-n odd and Z_2
for m-n even.Comment: 13 pages, to appear in Fundamenta Mathematica
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