Topology of phi-convex domains in calibrated manifolds


Unal I.

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

  • Publication Type: Article / Article
  • Volume: 42 Issue: 2
  • Publication Date: 2011
  • Doi Number: 10.1007/s00574-011-0014-7
  • Title of Journal : BULLETIN OF THE BRAZILIAN MATHEMATICAL SOCIETY
  • Page Numbers: pp.259-275

Abstract

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.