Abstract
In this paper, we prove the nonexistence of stable integral currents in compact oriented warped product pointwise semi-slant submanifold M-n of a complex space form (M) over tilde (4 epsilon) under extrinsic conditions which involve the Laplacian, the squared norm gradient of the warped function, and pointwise slant functions. We show that i-the homology groups of M-n are vanished. As applications of homology groups, we derive new topological sphere theorems for warped product pointwise semi-slant submanifold M-n, in which M-n is homeomorphic to a sphere S-n if n >= 4 and if n=3, then M-3 is homotopic to a sphere S-3 under the assumption of extrinsic conditions. Moreover, the same results are generalized for CR-warped product submanifolds.