Topology of phi-convex domains in calibrated manifolds

Unal I.

BULLETIN OF THE BRAZILIAN MATHEMATICAL SOCIETY, vol.42, no.2, pp.259-275, 2011 (SCI-Expanded) identifier identifier


In [5], Harvey and Lawson showed that for any calibration phi there is an integer bound for the homotopy dimension of a strictly phi-convex domain and constructed a method to get these domains by using phi-free submanifolds. Here, we show how to get examples of phi-free submanifolds with different homotopy types for the quaternion calibration in H(n), associative calibration, and coassociative calibration in G(2) manifolds. Hence we give examples of strictly phi-convex domains with different homotopy types allowed by Morse Theory.