explicitly exhibiting that SL ( 2 , C ) is simply connected. But SO ( 3 ; 1 ) ≅ ≅ SL ( 2 , C ) / { ± ± I } , where { ± ± I } is the center of SL ( 2 , C ) . Identifying λ and − λ amounts to identifying u with − u, which in turn amounts to identifying antipodal points on S 3 . Thus topologically, SO ( 3 ; 1 ) ≅ ≅ R 3 × × ( S 3 / Z 2 ) ,