We construct special handle decompositions for a compact connected PL manifold with non empty boundary and study the associated topological invariants. As a consequence, we characterize the unknot in the (n+2)-sphere (n less or equal 2) as the unique n-knot whose complement has genus one. Then we obtain a simple geometric proof of the non cancellation theorem for tame n-knots in the (n+2)-sphere, for n less or equal 2.
Splittings of manifolds with boundary and related invariants / Cavicchioli, Alberto; Ruini, Beatrice. - In: RENDICONTI DELL'ISTITUTO DI MATEMATICA DELL'UNIVERSITÀ DI TRIESTE. - ISSN 0049-4704. - STAMPA. - 25 Fasc. I-II:(1993), pp. 67-87.
Splittings of manifolds with boundary and related invariants
CAVICCHIOLI, Alberto;RUINI, Beatrice
1993
Abstract
We construct special handle decompositions for a compact connected PL manifold with non empty boundary and study the associated topological invariants. As a consequence, we characterize the unknot in the (n+2)-sphere (n less or equal 2) as the unique n-knot whose complement has genus one. Then we obtain a simple geometric proof of the non cancellation theorem for tame n-knots in the (n+2)-sphere, for n less or equal 2.
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