Date: Sun, 31 Jan 1999 20:08:33 -0500 (EST) From: Gustavo Granja Subject: algorithms for htpy groups Since there seem to be so many people interested in algorithms for computing homotopy groups I thought I should mention the paper "The Computability Problem in Algebraic Topology" by F. Sergeraert in Advances in Mathematics 104 (1994) 1-29. The author has a theory of "effective homology". According to him this theory makes it possible to write programs to compute the usual algebraic-topological invariants of any reasonable space. He also says that his methods have been used to compute previously unknown invariants. In a recent preprint "On the homotopy type of infinite stunted projective spaces" by F. Cohen and R. Levi, (Preprint no. 395, Nov. 98 CRM) the authors mention (p. 10) that certain calculations of homotopy groups in their paper corroborate calculations made by Sergeraert and his coauthors and they give as reference a paper by Sergeraert and Smirnov which is to appear. Gustavo Granja