Characteristic Zero Loop Space Homology and Enveloping Algebras

The work contains the doctoral dissertation the author presented at Universite Catholique de Louvain in January, 2000. The first two chapters deal with extensions of results of Quillen, Anick, Scheerer-Tanre and Halperin on the homology of differential graded Lie algebras and their universal enveloping algebras. The last two chapters deal with characteristic zero loop space homology of two-cones (cofibers of maps between wedges of spheres) and fat wedges of spheres, respectively. Numerous examples are discussed in careful detail. The topic may interest rational homotopists, Lie algebraists and, possibly, some group theorists.

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The author has received his Ph.D. from Universite Catholique de Louvain, Belgium, in 2000, under Professor Yves Felix. He is now with the Institute of Mathematics of the Romanian Academy. His main field is algebraic topology and has more than a passing interest in differential topology and geometry, geometric combinatorics and graph theory.