A linear representation of the mapping class group and the theory of winding numbers
dc.contributor.author | Trapp, Rolland | en_US |
dc.date.accessioned | 2006-04-10T15:21:32Z | |
dc.date.available | 2006-04-10T15:21:32Z | |
dc.date.issued | 1992-01-02 | en_US |
dc.identifier.citation | Trapp, Rolland (1992/01/02)."A linear representation of the mapping class group and the theory of winding numbers." Topology and its Applications 43(1): 47-64. <http://hdl.handle.net/2027.42/30247> | en_US |
dc.identifier.uri | http://www.sciencedirect.com/science/article/B6V1K-47RBT9T-V/2/3e3b760c7a61f9d98477c8d3e989a0b6 | en_US |
dc.identifier.uri | https://hdl.handle.net/2027.42/30247 | |
dc.description.abstract | This paper describes a linear representation F of the mapping class group , of an orientable surface S with one boundary component. The representation F extends the symplectic representation, and is defined for surfaces of arbitrary genus g> 1. The main tools used to define F are crossed homomorphisms which are defined using nonvanishing vector fields X on S, and the theory of winding numbers of curves on surfaces described by Chillingworth in [1,2]. These crossed homomorphisms were essentially described by Morita in [6]. A geometric interpretation of F is then given. If T1S denotes the unit tangent bundle of S1 then F records the action of on H1(T1S;Z). The kernel of F is then characterized using knowledge of the crossed homomorphisms ex. If matrix entries are taken modulo 2g-2, the representation F factors through the mapping class group of a closed orientable surface of genus g > 1. Thus F induces representations of Dn of for any n[-45 degree rule]2g-2. The Dn were discovered by Sipe in [7, 8], and it is noted that her characterization of the image of Dn carries over to the integer valued case. The structure found in characterizing ker F is then used to study ker Dn. In particular, it is shown that a uotient of ker Dn is a semidirect product for each even n dividing 2g-2. | en_US |
dc.format.extent | 2148492 bytes | |
dc.format.extent | 3118 bytes | |
dc.format.mimetype | application/pdf | |
dc.format.mimetype | text/plain | |
dc.language.iso | en_US | |
dc.publisher | Elsevier | en_US |
dc.title | A linear representation of the mapping class group and the theory of winding numbers | en_US |
dc.type | Article | en_US |
dc.rights.robots | IndexNoFollow | en_US |
dc.subject.hlbsecondlevel | Mathematics | en_US |
dc.subject.hlbtoplevel | Science | en_US |
dc.description.peerreviewed | Peer Reviewed | en_US |
dc.contributor.affiliationum | Department of Mathematics., University of Michigan, Ann Arbor, MI, 48109-1003, USA | en_US |
dc.description.bitstreamurl | http://deepblue.lib.umich.edu/bitstream/2027.42/30247/1/0000642.pdf | en_US |
dc.identifier.doi | http://dx.doi.org/10.1016/0166-8641(92)90153-Q | en_US |
dc.identifier.source | Topology and its Applications | en_US |
dc.owningcollname | Interdisciplinary and Peer-Reviewed |
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