  The paper is devoted to a detailed exposition of results outlined in author's
1983 note "On the virtual cohomology dimension of the Teichm\"uller modular
group". The paper includes the full proofs and a discussion of the context
which motivated both the results and the methods used. The reminiscences
included into the last section are an integral part of this discussion. A key
idea is to use the simply-connectedness of the Hatcher-Thurston complex. This
idea was hardly developed further, but still keeps a promise.
