caa a22 4500 386372365 CHVBK 20180307112002.0 cr unu---uuuuu 161130e198905 xx s 000 0 eng 10.1017/S001708950000776X doi S001708950000776X pii (NATIONALLICENCE)cambridge-10.1017/S001708950000776X Humphries Stephen P. Department of Mathematics, Brigham Young University, Provo, Utah 84602, USA Free products in mapping class groups generated by Dehn twists [Elektronische Daten] [Stephen P. Humphries] Let F be an orientable surface with or without boundary and let M(F) be the mapping class group of F, i.e. the group of isotopy classes of orientation preserving diffeomorphisms of F. To each essential simple closed curve c on F we can associate an element C of M(F) called the Dehn twist about c. We refer the reader to [1] for definitions. It is well known (see [1]) that, at least in the case where F has no more than one boundary component, M(F) is generated by Dehn twists. Further, there are important subgroups of M(F) which are also generated by Dehn twists or simple products of Dehn twists; for example the Torelli group, the kernel of the homology action map M(F)→ Aut(H1(F;Z)) = Sp(H1(F;Z)), where Sp(H1(F;Z)) denotes the symplectic group, is known to be generated by Dehn twists about bounding curves and by "bounding pairs”. See [8] for proofs and definitions. Also Dehn twists crop up as geometric monodromy maps associated to Picard-Lefschetz vanishing cycles for plane curve singularities (see [5]). Copyright © Glasgow Mathematical Journal Trust 1989 Glasgow Mathematical Journal Cambridge University Press 31/2(1989-05), 213-218 0017-0895 31:2<213 1989 31 GMJ https://doi.org/10.1017/S001708950000776X text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1017/S001708950000776X text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Humphries Stephen P. Department of Mathematics, Brigham Young University, Provo, Utah 84602, USA NATIONALLICENCE 773 0- Glasgow Mathematical Journal Cambridge University Press 31/2(1989-05), 213-218 0017-0895 31:2<213 1989 31 GMJ CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-cambridge