Title: Surgery groups of knot and link complements
(joint
work with C. S. Aravinda and F. T. Farrell)
Abstract: In this article we prove a conjecture due to S. Cappell
which
says that the surgery groups of the fundamental group of any knot
complement
in the 3-sphere are isomorphic to the surgery groups of the infinite
cyclic
group. We also compute explicitly the surgery groups of the fundamental
group of any link complement in the 3-sphere. We use existence of
nonpositively
curved Riemannian metric in the interior of the manifolds and the
Topological
Rigidity Theorem of Farrell and Jones to prove the results.
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Title: Surgery groups of submanifolds of S^3
(appeared in Topology
Appl., 100/2-3 (2000) 223-227).
Abstract: In this note we prove that the homotopy-topological
structure
set vanish for any irreducible sub-complex complement in the 3-sphere
with
incompressible boundary. As a consequence we calculate explicitly the
surgery
groups of any sub-complex complement.
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