To Dmitry Borisovich Fuchs, on his 60-th birthday This paper is a sequel to [MSV]. It consists of three parts. The first part is an expanded version of the last section of [MSV] 1. We give here certain construction of vertex algebras which includes in particular the ones appearing in loc. cit.

We show that there are two homotopy types of PD3 -complexes with fundamental group S3 ∗Z/2Z S3 , and give explicit constructions for each, which differ only in the attachment of the top cell. AMS Classification 57P10; 55M05