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Summary: GENUS AND DEGREES OF TORUS KNOTS IN CP2
MOHAMED AIT NOUH
Department of Mathematics,
California State University Channel Islands
One University Drive, Camarillo, CA 93102
e-mail: mohamed.aitnouh@csuci.edu
ABSTRACT
The CP2-genus of a knot K is the minimal genus over all isotopy classes of smooth, com-
pact, connected and oriented surfaces properly embedded in CP2
- intB4
with bound-
ary K. We compute the CP2-genus and realizable degrees of all (±2, q)-torus knots for
3 q 11 . The proofs use gauge theory and twisting operations on knots.
1. Introduction
Throughout this paper, we work in the smooth category. All orientable manifolds will be as-
sumed to be oriented unless otherwise stated. A knot is a smooth embedding of S1 into the 3-sphere
S3 = R3
{±}. All knots are oriented. Recall that CP2
is the closed 4-manifold obtained by the
free action of C
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