On K3-Thurston 7-manifolds and their deformation space: A case study with remarks on general K3T and M-theory compactification

M-theory suggests the study of 11-dimensional space-times compactified on some 7-manifolds. From its intimate relation to superstrings, one possible class of such 7-manifolds are those that have Calabi-Yau threefolds as boundary. In this article, we construct a special class of such 7-manifolds, named as K3-Thurston (K3T) 7manifolds. The factor from the K3 part of the deformation space of these K3T 7manifolds admits a Kähler structure, while the factor of the deformation space from the Thurston part admits a special Kähler structure. The latter rings with the nature of the scalar manifold of a vector multiplet in an N = 2 d = 4 supersymmetric gauge theory. Remarks and examples on more general K3T 7-manifolds and issues to possible interfaces of K3T to M-theory are also discussed.