Topology of <Emphasis Type="Italic">ϕ</Emphasis>-convex domains in calibrated manifolds

In 5], Harvey and Lawson showed that for any calibration ϕ there is an integer bound for the homotopy dimension of a strictly ϕ-convex domain and constructed a method to get these domains by using ϕ-free submanifolds. Here, we show how to get examples of ϕ-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 ϕ-convex domains with different homotopy types allowed by Morse Theory.