A note on the cohomology ring of the oriented Grassmann manifolds
Archivum Mathematicum (2019)
- Volume: 055, Issue: 5, page 319-331
- ISSN: 0044-8753
Access Full Article
top
Abstract
topHow to cite
topRusin, Tomáš. "A note on the cohomology ring of the oriented Grassmann manifolds $\widetilde{G}_{n,4}$." Archivum Mathematicum 055.5 (2019): 319-331. <http://eudml.org/doc/294713>.
@article{Rusin2019,
abstract = {We use known results on the characteristic rank of the canonical $4$–plane bundle over the oriented Grassmann manifold $\widetilde\{G\}_\{n,4\}$ to compute the generators of the $\mathbb \{Z\}_2$–cohomology groups $H^j(\widetilde\{G\}_\{n,4\})$ for $n=8,9,10,11$. Drawing from the similarities of these examples with the general description of the cohomology rings of $\widetilde\{G\}_\{n,3\}$ we conjecture some predictions.},
author = {Rusin, Tomáš},
journal = {Archivum Mathematicum},
keywords = {oriented Grassmann manifold; characteristic rank; Stiefel-Whitney class},
language = {eng},
number = {5},
pages = {319-331},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {A note on the cohomology ring of the oriented Grassmann manifolds $\widetilde\{G\}_\{n,4\}$},
url = {http://eudml.org/doc/294713},
volume = {055},
year = {2019},
}
TY - JOUR
AU - Rusin, Tomáš
TI - A note on the cohomology ring of the oriented Grassmann manifolds $\widetilde{G}_{n,4}$
JO - Archivum Mathematicum
PY - 2019
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 055
IS - 5
SP - 319
EP - 331
AB - We use known results on the characteristic rank of the canonical $4$–plane bundle over the oriented Grassmann manifold $\widetilde{G}_{n,4}$ to compute the generators of the $\mathbb {Z}_2$–cohomology groups $H^j(\widetilde{G}_{n,4})$ for $n=8,9,10,11$. Drawing from the similarities of these examples with the general description of the cohomology rings of $\widetilde{G}_{n,3}$ we conjecture some predictions.
LA - eng
KW - oriented Grassmann manifold; characteristic rank; Stiefel-Whitney class
UR - http://eudml.org/doc/294713
ER -
References
top- Basu, S., Chakraborty, P., On the cohomology ring and upper characteristic rank of Grassmannian of oriented 3-planes, arXiv:1712.00284v1 [math.AT].
- Borel, A., 10.1007/BF02564561, Comment. Math. Helv. 27 (1953), 165–197. (1953) MR0057541DOI10.1007/BF02564561
- Korbaš, J., 10.36045/bbms/1267798499, Bull. Belg. Math. Soc. Simon Stevin 17 (2010), 69–81. (2010) MR2656672DOI10.36045/bbms/1267798499
- Korbaš, J., Rusin, T., A note on the -cohomology algebra of oriented Grassmann manifolds, Rend. Circ. Mat. Palermo, II. Ser. 65 (2016), 507–517. (2016) MR3571326
- Korbaš, J., Rusin, T., 10.4310/HHA.2016.v18.n2.a4, Homology Homotopy Appl. 18 (2) (2016), 71–84. (2016) MR3518983DOI10.4310/HHA.2016.v18.n2.a4
- Milnor, J., Stasheff, J., Characteristic Classes, Princeton University Press, Princeton, N. J.; University of Tokyo Press, Tokyo, 1974. (1974) Zbl0298.57008MR0440554
- Naolekar, A.C., Thakur, A.S., 10.2478/s12175-014-0289-4, Math. Slovaca 64 (2014), 1525–1540. (2014) MR3298036DOI10.2478/s12175-014-0289-4
- Prvulović, B.I., Radovanović, M., 10.4064/fm470-3-2018, Fundamenta Mathematicae 244 (2019), 167–190. (2019) MR3874670DOI10.4064/fm470-3-2018
- Stong, R.E., 10.1016/0022-4049(84)90029-X, J. Pure Appl. Alg. 33 (1984), 97–103. (1984) MR0750235DOI10.1016/0022-4049(84)90029-X
NotesEmbed ?
topYou must be logged in to post comments.
To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.