PL involutions of fibered 3-manifolds

Abstract

Let h be a PL involution of F × [ 0 , 1 ] F \times [0,1] such that h ( F × { 0 , 1 } ) = F × { 0 , 1 } h(F \times \{ 0,1\} ) = F \times \{ 0,1\} , where F is a compact 2-manifold. It is shown that h is equivalent to an involution h ′ h’ of the form h ′ ( x , t ) = ( g ( x ) , λ ( t ) ) h’(x,t) = (g(x),\lambda (t)) . This result is applied to classify the PL involutions of closed, orientable, Seifert manifolds when the fixed-point set contains a two-dimensional component of negative characteristic.