Homology of manifolds obtained by Dehn surgery on knots in lens spaces

Abstract

The question whether or not a Dehn surgery on a knot in a lens space yields a lens space of the same order is investigated with homoiogical techniques.Determining the first homology group of the lens space after surgery and of its covering yields some necessary conditions on the knot and the surgery curve. Application of these results along with a calculation of Seifert invariants answers the question completely for surgery on torus knots along nullhomological curves. 431 J. Knot Theory Ramifications 2000.09:431-442. Downloaded from www.worldscientific.com by THE UNIVERSITY OF OKLAHOMA on 02/03/15. For personal use only.