论文信息 - Constructive algebraic topology

Constructive algebraic topology

Abstract The classical “computation” methods in Algebraic Topology most often work by means of highly infinite objects and in fact are not constructive. Typical examples are shown to describe the nature of the problem. The Rubio–Sergeraert solution for Constructive Algebraic Topology is recalled. This is not only a theoretical solution: the concrete computer program Kenzo has been written down which precisely follows this method. This program has been used in various cases, opening new research subjects and producing in several cases significant results unreachable by hand. In particular the Kenzo program can compute the first homotopy groups of a simply connected arbitrary simplicial set.

Julio Rubio | Francis Sergeraert

[1] Justin R. Smith. Iterating the Cobar Construction , 1994 .

[2] Weishu Shih,et al. Homologie des espaces fibrés , 1962 .

[3] Hans-Joachim Baues,et al. Geometry of Loop Spaces and the Cobar Construction , 1980 .

[4] John McCleary,et al. User's Guide to Spectral Sequences , 1985 .

[5] Ioan Mackenzie James,et al. Handbook of algebraic topology , 1995 .

[6] S. I. Gelʹfand,et al. Methods of Homological Algebra , 1996 .

[7] J. Adams,et al. ON THE COBAR CONSTRUCTION. , 1956, Proceedings of the National Academy of Sciences of the United States of America.

[8] Guy L. Steele,et al. Common Lisp the Language , 1984 .

[9] Gunnar E. Carlsson,et al. CHAPTER 13 – Stable Homotopy and Iterated Loop Spaces , 1995 .

[10] Dominique Dancète,et al. Sur l'itération de la construction Cobar , 1999 .

[11] Edgar H. Brown,et al. FINITE COMPUTABILITY OF POSTNIKOV COMPLEXES , 1957 .

[12] Rolf Schön,et al. Effective Algebraic Topology , 1991 .

[13] Edgar H. Brown,et al. Twisted Tensor Products, I , 1959 .

[14] Francis Sergeraert,et al. The Computability Problem in Algebraic Topology , 1994 .