Strongly pseudoconvex handlebodies

We give an explicit construction of special strongly pseudoconvex domains in C^n of handlebody type, i.e., domains which are small tubes surrounding the union of a quadratic strongly pseudoconvex domain with an attached totally real handle. Among other results, we give another proof of Lemma 3.4.3. from the paper of Y. Eliashberg, “Topological characterization of Stein manifolds of dimension $>2$”, Internat. J. Math., 1 (1990), 29–46.