Title: Surgery groups of knot and link complements
work with C. S. Aravinda and F. T. Farrell)
Abstract: In this article we prove a conjecture due to S. Cappell
says that the surgery groups of the fundamental group of any knot
in the 3-sphere are isomorphic to the surgery groups of the infinite
group. We also compute explicitly the surgery groups of the fundamental
group of any link complement in the 3-sphere. We use existence of
curved Riemannian metric in the interior of the manifolds and the
Rigidity Theorem of Farrell and Jones to prove the results.
for the full article.
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
set vanish for any irreducible sub-complex complement in the 3-sphere
incompressible boundary. As a consequence we calculate explicitly the
groups of any sub-complex complement.