Decorated Teichmüller theory of bordered surfaces
By R. Penner. 2002
74 citations recorded by the source corpus.
This paper extends the decorated Teichmuller theory developed before for punctured surfaces to the setting of “bordered” surfaces, i.e., surfaces with boundary, and there is non-trivial new structure discovered. Beyond this, the main new result of this paper identifies an open dense subspace of the arc complex of a bordered surface up to proper homotopy equivalence with a certain quotient of the moduli space, namely, the quotient by the natural action of the positive reals by homothety on the hyperbolic lengths of geodesic boundary components. One tool in the proof is a homeomorphism between two versions of a “decorated” moduli space for bordered surfaces. The explicit homeomorphism relies upon points equidistant to suitable triples of horocycles.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/2b6e6fc1efce272b1552608ab3f08735cb3d9f95
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In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- A proof of a cyclic version of Deligne’s conjecture via Cacti (2004, background): “The length of a cyclec is the sum of the lengths of its edgeslength(c) = P f2cw({f,i(f)}).”
- On spineless cacti, Deligne's conjecture and Connes-Kreimer's Hopf algebra (2003, methodology): “As we are using cacti, this approach naturally lies within string topology on one hand and on the other hand it is embedded in the framework of a combinatorial description of the moduli space of surfaces with punctured boundaries via theArc operad [17,18,26,34].”
- Hochschild homology of structured algebras (2011, unknown): “Similarly, fat graphs with leaves define a chain complex for the moduli space of surfaces with fixed boundaries, or with fixed intervals in their boundaries (see Penner [32, 29], Godin [13], Costello [8, Sect.”
- Arc Operads and Arc Algebras (2002, background): “5 Remark It is the purpose of this remark to explain the geometry underlying Arc(F ) which was uncovered in [12, 13].”