A note on the cohomology ring of the oriented Grassmann manifolds ${\tilde{G}}_{n,4}$

@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 -