Editing Orthogonal group (section)

=== Fundamental group ===
In terms of [[algebraic topology]], for {{math|''n'' > 2}} the [[fundamental group]] of {{math|SO(''n'', '''R''')}} is [[Cyclic group|cyclic of order 2]],<ref>{{harvnb|Hall|2015}} Proposition 13.10</ref> and the [[spin group]] {{math|Spin(''n'')}} is its [[universal cover]]. For {{math|1=''n'' = 2}} the fundamental group is [[infinite cyclic]] and the universal cover corresponds to the  [[real line]] (the group {{math|Spin(2)}} is the unique connected [[double cover (topology)|2-fold cover]]).