caa a22 4500 445884754 CHVBK 20180317145555.0 cr unu---uuuuu 170323e20111201xx s 000 0 eng 10.1007/s10711-011-9584-1 doi (NATIONALLICENCE)springer-10.1007/s10711-011-9584-1 Separating twists and the Magnus representation of the Torelli group [Elektronische Daten] [Thomas Church, Aaron Pixton] The Magnus representation of the Torelli subgroup of the mapping class group of a surface is a homomorphism $${r: \fancyscript{I}_{g,1} \to {\rm GL}_{2g}(\mathbb{Z}H)}$$ . Here H is the first homology group of the surface. This representation is not faithful; in particular, Suzuki previously described precisely when the commutator of two Dehn twists about separating curves is in ker r. Using the trace of the Magnus representation, we apply a new method of showing that two endomorphisms generate a free group to prove that the images of two positive separating multitwists under the Magnus representation either commute or generate a free group, and we characterize when each case occurs. Springer Science+Business Media B.V., 2011 Magnus representation nationallicence Separating twist nationallicence Torelli group nationallicence Church Thomas Department of Mathematics, University of Chicago, 60637, Chicago, IL, USA aut Pixton Aaron Mathematics Department, Princeton University, 08544, Princeton, NJ, USA aut Geometriae Dedicata Springer Netherlands 155/1(2011-12-01), 177-190 0046-5755 155:1<177 2011 155 10711 https://doi.org/10.1007/s10711-011-9584-1 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10711-011-9584-1 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Church Thomas Department of Mathematics, University of Chicago, 60637, Chicago, IL, USA aut NATIONALLICENCE 700 1- Pixton Aaron Mathematics Department, Princeton University, 08544, Princeton, NJ, USA aut NATIONALLICENCE 773 0- Geometriae Dedicata Springer Netherlands 155/1(2011-12-01), 177-190 0046-5755 155:1<177 2011 155 10711 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer