High distance Heegaard splittings from involutions

Fixed an oriented handlebody H = H(+) with boundary F, let eta(H(+))= H(-) be the mirror image of H(+) along F, so eta(F) is the boundary of H(-), for a map f :F -> F, we have a 3-manifold by gluing H(+) and H(-) along F with attaching map f, and denote it by M(f) = H(+) U(f: F -> F) H(-). In this note, we show that there are involutions f: F -> F which are also reducible, such that M(f) have arbitrarily high Heegaard distances. (C) 2010 Elsevier B.V. All rights reserved.