Highly connected embeddings in codimension two

Author:
Susan Szczepanski

Journal:
Trans. Amer. Math. Soc. **280** (1983), 139-159

MSC:
Primary 57R40; Secondary 57R67

DOI:
https://doi.org/10.1090/S0002-9947-1983-0712253-5

MathSciNet review:
712253

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Abstract: In this paper we study semilocal knots over into , that is, embeddings of a manifold into , the total space of a -disk bundle over a manifold , such that the restriction of the bundle projection to the submanifold is homotopic to a normal map of degree one, . We develop a new homology surgery theory which does not require homology equivalences on boundaries and, in terms of these obstruction groups, we obtain a classification (up to cobordism) of semilocal knots over into . In the simply connected case, the following geometric consequence follows from our classification. Every semilocal knot of a simply connected manifold in a bundle over is cobordant to the connected sum of the zero section of this bundle with a semilocal knot of the highly connected manifold into the trivial bundle over a sphere.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1983-0712253-5

Keywords:
Surgery,
cobordism of embeddings,
Hermitian forms,
highly connected maps and manifolds

Article copyright:
© Copyright 1983
American Mathematical Society