| Title:
|
On real flag manifolds with cup-length equal to its dimension (English) |
| Author:
|
Radovanović, Marko |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
70 |
| Issue:
|
2 |
| Year:
|
2020 |
| Pages:
|
299-310 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We prove that for any positive integers $n_1,n_2,\ldots ,n_k$ there exists a real flag manifold $F(1,\ldots ,1,n_1,n_2,\ldots ,n_k)$ with cup-length equal to its dimension. Additionally, we give a necessary condition that an arbitrary real flag manifold needs to satisfy in order to have cup-length equal to its dimension. (English) |
| Keyword:
|
cup-length |
| Keyword:
|
flag manifold |
| Keyword:
|
Lyusternik-Shnirel'man category |
| MSC:
|
14M15 |
| MSC:
|
55M30 |
| MSC:
|
57N65 |
| idZBL:
|
07217136 |
| idMR:
|
MR4111844 |
| DOI:
|
10.21136/CMJ.2019.0283-18 |
| . |
| Date available:
|
2020-06-17T12:29:50Z |
| Last updated:
|
2022-07-04 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/148229 |
| . |
| Reference:
|
[1] Berstein, I.: On the Lusternik-Schnirelmann category of Grassmannians.Math. Proc. Camb. Philos. Soc. 79 (1976), 129-134. Zbl 0315.55011, MR 0400212, 10.1017/S0305004100052142 |
| Reference:
|
[2] Borel, A.: La cohomologie mod 2 de certains espaces homogènes.Comment. Math. Helv. 27 (1953), 165-197 French. Zbl 0052.40301, MR 0057541, 10.1007/BF02564561 |
| Reference:
|
[3] Hiller, H. L.: On the cohomology of real Grassmanians.Trans. Am. Math. Soc. 257 (1980), 521-533. Zbl 0462.57021, MR 0552272, 10.2307/1998310 |
| Reference:
|
[4] Horanská, L'., Korbaš, J.: On cup products in some manifolds.Bull. Belg. Math. Soc. -- Simon Stevin 7 (2000), 21-28. Zbl 0956.55010, MR 1741743, 10.36045/bbms/1103055716 |
| Reference:
|
[5] Korbaš, J., Lörinc, J.: The $\mathbb Z_2$-cohomology cup-length of real flag manifolds.Fundam. Math. 178 (2003), 143-158. Zbl 1052.55006, MR 2029922, 10.4064/fm178-2-4 |
| Reference:
|
[6] Petrović, Z. Z., Prvulović, B. I., Radovanović, M.: On maximality of the cup-length of flag manifolds.Acta Math. Hung. 149 (2016), 448-461. Zbl 1389.57006, MR 3518647, 10.1007/s10474-016-0625-y |
| Reference:
|
[7] Petrović, Z. Z., Prvulović, B. I., Radovanović, M.: Gröbner bases for (partial) flag manifolds.(to appear) in J. Symb. Comput. MR 4109710, 10.1016/j.jsc.2019.06.008 |
| Reference:
|
[8] Radovanović, M.: Gröbner bases for some flag manifolds and applications.Math. Slovaca 66 (2016), 1065-1082. Zbl 1399.13029, MR 3602604, 10.1515/ms-2016-0204 |
| Reference:
|
[9] Radovanović, M.: On the $\Bbb Z_2$-cohomology cup-length of some real flag manifolds.Filomat 30 (2016), 1577-1590. Zbl 06749816, MR 3530103, 10.2298/FIL1606577R |
| Reference:
|
[10] Stong, R. E.: Cup products in Grassmannians.Topology Appl. 13 (1982), 103-113. Zbl 0469.55005, MR 0637432, 10.1016/0166-8641(82)90012-8 |
| . |
