Homotopy groups of quasi-spheres and applications to indefinite orthogonal groups

Xiangjia Kong, Reese Lance, Franklin Rea

In this note, we present a new proof of the isomorphism ${\pi }_1(S{O}^{+}(p,q))\cong {\pi }_1(SO(p))\times {\pi }_1(SO(q))$ using the long exact sequence associated to a fibration. While this formu…