Orientation reversing involutions on closed 3-manifolds

Masako Kobayashi
Note that ίί^M; Z^H^M^ z}®H γ (M 2 \ Z)®Z. Constructions. Proof of Theorem 3. Let E ly E 2ί •• J E m be the components of E. Consider a handlebody V l such that dV 1 = E 1 . Let F 2 , F 3J •-, F w be murtually disjoint handlebodies contained in v λ such that the natural homomorphism H^Vi] Z}-+H λ (V λ \ Z} is trivial. Let M l =V l -U V { . Then the double of M 19 DM ly has an orientation reversing involtuion r interchanging the copies of M! with Fix(τ, DM^)= U V έ . Note that H^DM^ Z) is a free
more » ... H^DM^ Z) is a free abelian group of rank
doi:10.18910/12496 fatcat:w5qk7brztja3rf6hcbfjmuhteu