 
Summary: Minimal genus problem: New approach
Mohamed AIT NOUH
Department of Mathematics,
University of California at Santa Barbara
Santa Barbara, CA 93106
Email: aitnouh@math.ucsb.edu
Abstract
The minimal genus problem of connected sums of 4manifolds and the minimal slice genus of
knots in CP 2 are treated. The approach used is twisting operations on knots in S3.
We give an upper bound of the smooth slice genus of lefthanded torus knots in CP 2 and we
study the smooth slice genus of the family of (2, q)torus knots in CP 2 for any q 3.
T. Lawson conjectured in [23] that the minimal genus of (m, n) H2(CP2#CP2) is given by
(m1
2 ) + (n1
2 ) this is the genus realized by the connected sum of algebraic curves in each factor.
T. Lawson also conjectured in [23] that if X = X1#X2 is the connected sum of two symplectic
4manifolds with b+
2 3, and if (a, b) H2(X) = H2(X1)H2(X2) satisfies a.a 0 and b.b 0,
then the minimal genus for this class is the sum of the minimal genus for the class a and the
minimal genus for the class b.
