Equivariant pl embeddings of spheres

Codimension Two Pl Embeddings of Spheres with Nonstandard Regular Neighborhoods

Abstract. For a given polyhedron K ⊂ M the notation RM (K) denotes a regular neighborhood of K in M . We study the following problem: find all pairs (m,k) such that if K is a compact k-polyhedron and M a PL m-manifold, then RM (fK) ∼= RM (gK), for each two homotopic PL embeddings f, g : K → M . We prove that R Sk+2 (S) 6∼= S × D for each k ≥ 2 and some PL sphere S ⊂ S (even for any PL sphere S ...

Equivariant Dierential Embeddings

Equivariant differential embeddings

Takens Dynamical Systems and Turbulence, Lecture Notes in Mathematics, edited by D. A. Rand and L. S. Young Springer-Verlag, New York, 1981 , Vol. 898, pp. 366–381 has shown that a dynamical system may be reconstructed from scalar data taken along some trajectory of the system. A reconstruction is considered successful if it produces a system diffeomorphic to the original. However, if the origi...

Poincaré Embeddings of Spheres

Given a 1-connected Poincaré duality space M of dimension 2p, with p > 2, we give criteria for deciding when homotopy classes S −→ M are represented by framed Poincaré embedded p-spheres.

On Embeddings of Spheres

Imbed a n w 1 sphere in an n sphere, and the complement is divided into two components. I t seems that the closure of each of the resulting components should be a topological w-cell. This statement isn't true. The classical counterexample (in dimension 3) is the Alexander Horned Sphere. I t was conjectured, however, that if one restricts one's attention to some class of well-behaved imbeddings,...