Rational LS category and its applications
- Resource Type
- Article
- Authors
- Félix, Yves; Halperin, Stephen
- Source
- Transactions of the American Mathematical Society; 1982, Vol. 273 Issue: 1 p1-37, 37p
- Subject
- Language
- ISSN
- 00029947; 10886850
Let $ S$-connected CW-complex of finite type and put $ {\text{ca}}{{\text{t}}_0}(S) = $ $ {S_{\mathbf{Q}}}$. It is shown that if $ \phi :S \to T$ $ {\pi _ \ast } \otimes {\mathbf{Q}}$ $ {\text{ca}}{{\text{t}}_0}(S) \leqslant {\text{ca}}{{\text{t}}_0}(T)$ is the fibre inclusion of a fibration. It is also shown that if $ {H^ \ast }(S;{\mathbf{Q}}) < \infty $ $ {\pi _ \ast }(S) \otimes {\mathbf{Q}} < \infty $ $ {\pi _k}(S) \otimes {\mathbf{Q}}$.