Gluing maps and cobordism maps in sutured monopole and instanton Floer theories

Abstract

Sutured monopole and instanton Floer homologies were introduced by Kronheimer and Mrowka (J. Differential Geom. 84 (2010) 301–364). We construct cobordism maps in these two theories and prove that such cobordism maps are functorial under the composition of cobordisms and have a duality property. Along with the construction, we also construct gluing maps in sutured monopole and instanton theories, which are of independent interest.