| 书目名称 | Rational Homotopy Theory | | 编辑 | Yves Félix,Stephen Halperin,Jean-Claude Thomas | | 视频video | | | 丛书名称 | Graduate Texts in Mathematics | | 图书封面 |  | | 描述 | as well as by the list of open problems in the final section of this monograph. The computational power of rational homotopy theory is due to the discovery by Quillen [135] and by Sullivan [144] of an explicit algebraic formulation. In each case the rational homotopy type of a topological space is the same as the isomorphism class of its algebraic model and the rational homotopy type of a continuous map is the same as the algebraic homotopy class of the correspond ing morphism between models. These models make the rational homology and homotopy of a space transparent. They also (in principle, always, and in prac tice, sometimes) enable the calculation of other homotopy invariants such as the cup product in cohomology, the Whitehead product in homotopy and rational Lusternik-Schnirelmann category. In its initial phase research in rational homotopy theory focused on the identi of these models. These included fication of rational homotopy invariants in terms the homotopy Lie algebra (the translation of the Whitehead product to the homo topy groups of the loop space OX under the isomorphism 11‘+1 (X) ~ 1I.(OX», LS category and cone length. Since then, however, work has concentrated | | 出版日期 | Textbook 2001 | | 关键词 | Algebraic topology; CW complex; Homotopy; Homotopy group; Loop group; cofibration; fibrations; homology; hom | | 版次 | 1 | | doi | https://doi.org/10.1007/978-1-4613-0105-9 | | isbn_softcover | 978-1-4612-6516-0 | | isbn_ebook | 978-1-4613-0105-9Series ISSN 0072-5285 Series E-ISSN 2197-5612 | | issn_series | 0072-5285 | | copyright | Springer Science+Business Media New York 2001 |
The information of publication is updating
|
|
发表于 2025-3-21 19:02:43
