Geodesic
On the cohomology of the classifying spaces of $SO(n)$-gauge groups over $S^2$
Homology, homotopy, and applications, Tome 26 (2024) no. 2, pp. 121-136.

Voir la notice de l'article provenant de la source International Press of Boston

Let $\mathcal{G}_\alpha (X,G)$ be the $G$-gauge group over a space $X$ corresponding to a map $\alpha : X \to B\mathcal{G}_1$. We compute the integral cohomology of $B\mathcal{G}_1 (S^2, SO(n))$ for $n = 3, 4$. We also show that the homology of $B\mathcal{G}_1 (S^2, SO(n))$ is torsion free if and only if $n \leqslant 4$. As an application, we classify the homotopy types of $SO(n)$-gauge groups over a Riemann surface for $n \leqslant 4$.
DOI : 10.4310/HHA.2024.v26.n2.a6
Classification : 55R40
Keywords: cohomology, gauge group, classifying space 
@article{HHA_2024_26_2_a5,
     author = {Yuki Minowa},
     title = {On the cohomology of the classifying spaces of $SO(n)$-gauge groups over $S^2$},
     journal = {Homology, homotopy, and applications},
     pages = {121--136},
     publisher = {mathdoc},
     volume = {26},
     number = {2},
     year = {2024},
     doi = {10.4310/HHA.2024.v26.n2.a6},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4310/HHA.2024.v26.n2.a6/}
}
TY  - JOUR
AU  - Yuki Minowa
TI  - On the cohomology of the classifying spaces of $SO(n)$-gauge groups over $S^2$
JO  - Homology, homotopy, and applications
PY  - 2024
SP  - 121
EP  - 136
VL  - 26
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4310/HHA.2024.v26.n2.a6/
DO  - 10.4310/HHA.2024.v26.n2.a6
LA  - en
ID  - HHA_2024_26_2_a5
ER  - 
%0 Journal Article
%A Yuki Minowa
%T On the cohomology of the classifying spaces of $SO(n)$-gauge groups over $S^2$
%J Homology, homotopy, and applications
%D 2024
%P 121-136
%V 26
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4310/HHA.2024.v26.n2.a6/
%R 10.4310/HHA.2024.v26.n2.a6
%G en
%F HHA_2024_26_2_a5
Yuki Minowa. On the cohomology of the classifying spaces of $SO(n)$-gauge groups over $S^2$. Homology, homotopy, and applications, Tome 26 (2024) no. 2, pp. 121-136. doi : 10.4310/HHA.2024.v26.n2.a6. http://geodesic.mathdoc.fr/articles/10.4310/HHA.2024.v26.n2.a6/

Cité par Sources :