A new invariant and parametric connected sum of embeddings
| dc.creator | Skopenkov, A. | |
| dc.date | 2005-09-27 | |
| dc.date | 2007-12-11 | |
| dc.date.accessioned | 2026-07-07T12:09:31Z | |
| dc.date.available | 2026-07-07T12:09:31Z | |
| dc.description | 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 to obtain new completeness results for the α-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 α-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. | |
| dc.description | 13 pages, to appear in Fundamenta Mathematicae | |
| dc.identifier | https://arxiv.org/abs/math/0509621 | |
| dc.identifier | http://arxiv.org/abs/math/0509621 | |
| dc.identifier | Fund. Math. 197 (2007), 253--269 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/209652 | |
| dc.subject | Geometric Topology | |
| dc.subject | Algebraic Topology | |
| dc.title | A new invariant and parametric connected sum of embeddings | |
| dc.type | text |