| Title:
|
An example of a fiber in fibrations whose Serre spectral sequences collapse (English) |
| Author:
|
Yamaguchi, Toshihiro |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
55 |
| Issue:
|
4 |
| Year:
|
2005 |
| Pages:
|
997-1001 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We give an example of a space $X$ with the property that every orientable fibration with the fiber $X$ is rationally totally non-cohomologous to zero, while there exists a nontrivial derivation of the rational cohomology of $X$ of negative degree. (English) |
| Keyword:
|
Sullivan minimal model |
| Keyword:
|
orientable fibration |
| Keyword:
|
TNCZ |
| Keyword:
|
negative derivation |
| MSC:
|
55P62 |
| MSC:
|
55R05 |
| MSC:
|
55T10 |
| idZBL:
|
Zbl 1081.55010 |
| idMR:
|
MR2184380 |
| . |
| Date available:
|
2009-09-24T11:29:48Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/128041 |
| . |
| Reference:
|
[1] I. Belegradek and V. Kapovitch: Obstructions to nonnegative curvature and rational homotopy theory.J. Amer. Math. Soc. 16 (2003), 259–284. MR 1949160 |
| Reference:
|
[2] Y. Félix, S. Halperin and J. C. Thomas: Rational Homotopy Theory.Springer GTM, 205, New York, 2001. MR 1802847 |
| Reference:
|
[3] S. Halperin: Rational fibrations, minimal models, and fibrings of homogeneous spaces.Trans. A.M.S. 244 (1978), 199–244. Zbl 0387.55010, MR 0515558, 10.1090/S0002-9947-1978-0515558-4 |
| Reference:
|
[4] M. Markl: Towards one conjecture on collapsing of the Serre spectral sequence.Rend. Circ. Mat. Palermo (2) Suppl. 22 (1990), 151–159. Zbl 0705.55007, MR 1061796 |
| Reference:
|
[5] W. Meier: Rational universal fibrations and flag manifolds.Math. Ann. 258 (1982), 329–340. Zbl 0466.55012, MR 0649203, 10.1007/BF01450686 |
| Reference:
|
[6] M. Schlessinger and J. Stasheff: Deformation theory and rational homotopy type.Preprint. |
| Reference:
|
[7] D. Sullivan: Infinitesimal computations in topology.Publ. I.H.E.S. 47 (1977), 269–331. Zbl 0374.57002, MR 0646078, 10.1007/BF02684341 |
| . |
