Mathematical Sciences: Rational Homotropy Theory

David Anick将继续他在有理同伦理论方面的研究，既因为它的内在兴趣，也因为它在积分同伦上的应用。主要方法将是使用空间的代数模型（Quillen, Sullivan, Adams-Hilton）；循环空间分解（Hilton-Milnor, Cohen-Moore- Neisendorfer, Selick）；庞加莱系列（Roos-Lofwall, Felix- Thomas-Halperin）。对拓扑代数工具的这种检验的真正应用，首先需要将这些工具应用于几何拓扑问题，然后将结果应用于理论物理等领域。

David Anick will continue his research in rational homotopy theory, both for its intrinsic interest and for its applications to integral homotopy. The principal methods will be the use of algebraic models for spaces (Quillen, Sullivan, Adams-Hilton); loop space decompositions (Hilton-Milnor, Cohen-Moore- Neisendorfer, Selick); and Poincare series (Roos-Lofwall, Felix- Thomas-Halperin). True applications of such examinations of the algebraic tools of topology require first, applications of the tools to geometric topological problems, and then, applications of the results to, for example, theoretical physics.