A necessary condition for embedding a complex in
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Stavros Papastavridis (1979)
Fundamenta Mathematicae
A. Skopenkov (2007)
Fundamenta Mathematicae
We define an isotopy invariant of embeddings 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...
Lambrechts, Pascal, Stanley, Don (2005)
Algebraic & Geometric Topology
Akiko Shima (1998)
Revista Matemática Complutense
Let T be a torus in S4 and T* a projection of T. If the singular set Gamma(T*) consists of one disjoint simple closed curve, then T can be moved to the standard position by an ambient isotopy of S4.
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