Matches in SemOpenAlex for { <https://semopenalex.org/work/W2051264796> ?p ?o ?g. }
Showing items 1 to 70 of
70
with 100 items per page.
- W2051264796 endingPage "2725" @default.
- W2051264796 startingPage "2713" @default.
- W2051264796 abstract "The mapping class group of a surface with one boundary component admits numerous interesting representations including a representation as a group of automorphisms of a free group and as a group of symplectic transformations. Insofar as the mapping class group can be identified with the fundamental group of Riemann's moduli space, it is furthermore identified with a subgroup of the fundamental path groupoid upon choosing a basepoint. A combinatorial model for this, the mapping class groupoid, arises from the invariant cell decomposition of Teichmüller space, whose fundamental path groupoid is called the Ptolemy groupoid. It is natural to try to extend representations of the mapping class group to the mapping class groupoid, i.e., to construct a homomorphism from the mapping class groupoid to the same target that extends the given representations arising from various choices of basepoint. Among others, we extend both aforementioned representations to the groupoid level in this sense, where the symplectic representation is lifted both rationally and integrally. The techniques of proof include several algorithms involving fatgraphs and chord diagrams. The former extension is given by explicit formulae depending upon six essential cases, and the kernel and image of the groupoid representation are computed. Furthermore, this provides groupoid extensions of any representation of the mapping class group that factors through its action on the fundamental group of the surface including, for instance, the Magnus representation and representations on the moduli spaces of flat connections." @default.
- W2051264796 created "2016-06-24" @default.
- W2051264796 creator A5021791172 @default.
- W2051264796 creator A5073992999 @default.
- W2051264796 creator A5059133247 @default.
- W2051264796 date "2009-11-01" @default.
- W2051264796 modified "2023-10-05" @default.
- W2051264796 title "Groupoid extensions of mapping class representations for bordered surfaces" @default.
- W2051264796 cites W1482125263 @default.
- W2051264796 cites W1565163390 @default.
- W2051264796 cites W1986441888 @default.
- W2051264796 cites W1993175250 @default.
- W2051264796 cites W1997290951 @default.
- W2051264796 cites W2003514224 @default.
- W2051264796 cites W2003979509 @default.
- W2051264796 cites W2007484848 @default.
- W2051264796 cites W2054606149 @default.
- W2051264796 cites W2313637748 @default.
- W2051264796 cites W4292101339 @default.
- W2051264796 doi "https://doi.org/10.1016/j.topol.2009.08.001" @default.
- W2051264796 hasPublicationYear "2009" @default.
- W2051264796 type Work @default.
- W2051264796 sameAs 2051264796 @default.
- W2051264796 citedByCount "13" @default.
- W2051264796 countsByYear W20512647962012 @default.
- W2051264796 countsByYear W20512647962014 @default.
- W2051264796 countsByYear W20512647962015 @default.
- W2051264796 countsByYear W20512647962016 @default.
- W2051264796 countsByYear W20512647962020 @default.
- W2051264796 countsByYear W20512647962022 @default.
- W2051264796 crossrefType "journal-article" @default.
- W2051264796 hasAuthorship W2051264796A5021791172 @default.
- W2051264796 hasAuthorship W2051264796A5059133247 @default.
- W2051264796 hasAuthorship W2051264796A5073992999 @default.
- W2051264796 hasBestOaLocation W20512647961 @default.
- W2051264796 hasConcept C136119220 @default.
- W2051264796 hasConcept C154945302 @default.
- W2051264796 hasConcept C202444582 @default.
- W2051264796 hasConcept C2777212361 @default.
- W2051264796 hasConcept C33923547 @default.
- W2051264796 hasConcept C41008148 @default.
- W2051264796 hasConceptScore W2051264796C136119220 @default.
- W2051264796 hasConceptScore W2051264796C154945302 @default.
- W2051264796 hasConceptScore W2051264796C202444582 @default.
- W2051264796 hasConceptScore W2051264796C2777212361 @default.
- W2051264796 hasConceptScore W2051264796C33923547 @default.
- W2051264796 hasConceptScore W2051264796C41008148 @default.
- W2051264796 hasIssue "17" @default.
- W2051264796 hasLocation W20512647961 @default.
- W2051264796 hasLocation W20512647962 @default.
- W2051264796 hasLocation W20512647963 @default.
- W2051264796 hasOpenAccess W2051264796 @default.
- W2051264796 hasPrimaryLocation W20512647961 @default.
- W2051264796 hasRelatedWork W1587224694 @default.
- W2051264796 hasRelatedWork W1979597421 @default.
- W2051264796 hasRelatedWork W2007980826 @default.
- W2051264796 hasRelatedWork W2061531152 @default.
- W2051264796 hasRelatedWork W2077600819 @default.
- W2051264796 hasRelatedWork W2142036596 @default.
- W2051264796 hasRelatedWork W2911598644 @default.
- W2051264796 hasRelatedWork W3002753104 @default.
- W2051264796 hasRelatedWork W4225152035 @default.
- W2051264796 hasRelatedWork W4245490552 @default.
- W2051264796 hasVolume "156" @default.
- W2051264796 isParatext "false" @default.
- W2051264796 isRetracted "false" @default.
- W2051264796 magId "2051264796" @default.
- W2051264796 workType "article" @default.