Rational homotopy theory
Rational homotopy theory
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DOI：
10.2307/1970725
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发表时间：
1969-09
影响因子：
4.9
通讯作者：
D. Quillen
中科院分区：
文献类型：
--
作者：
D. Quillen
当i ≥ 1时，它们确实是群，当i ≥ 2时，它们甚至是交换群，它们携带了关于X的同伦类型的大量信息。然而，即使对于容易定义的空间（如球体），它们也很难计算。即使在低维情况下，也很难在球面的同伦群中看到清晰的模式;特别是挠率表现出一种看似疯狂的行为。这表明，在第一步中，忽略同伦群中的挠率，只考虑有理同伦群（用Q张量的同伦群）可能是一个好主意。
For i ≥ 1 they are indeed groups, for i ≥ 2 even abelian groups, which carry a lot of information about the homotopy type of X. However, even for spaces which are easy to define (like spheres), they can be very hard to compute. Even in low dimensions it is difficult to see a clear pattern among the homotopy groups of spheres; especially the torsion shows a seemingly wild behaviour. This suggests that in a first step it might be a good idea to ignore the torsion in the homotopy groups and to just consider the rational homotopy groups (the homotopy groups tensored with Q).