2,157 research outputs found
Arc Operads and Arc Algebras
Several topological and homological operads based on families of projectively
weighted arcs in bounded surfaces are introduced and studied. The spaces
underlying the basic operad are identified with open subsets of a
compactification due to Penner of a space closely related to Riemann's moduli
space. Algebras over these operads are shown to be Batalin-Vilkovisky algebras,
where the entire BV structure is realized simplicially. Furthermore, our basic
operad contains the cacti operad up to homotopy, and it similarly acts on the
loop space of any topological space. New operad structures on the circle are
classified and combined with the basic operad to produce geometrically natural
extensions of the algebraic structure of BV algebras, which are also computed.Comment: Published by Geometry and Topology at
http://www.maths.warwick.ac.uk/gt/GTVol7/paper15.abs.htm
Marked fatgraph complexes and surface automorphisms
Combinatorial aspects of the Torelli-Johnson-Morita theory of surface
automorphisms are extended to certain subgroups of the mapping class groups.
These subgroups are defined relative to a specified homomorphism from the
fundamental group of the surface onto an arbitrary group . For abelian,
there is a combinatorial theory akin to the classical case, for example,
providing an explicit cocycle representing the first Johnson homomophism with
target . Furthermore, the Earle class with coefficients in is
represented by an explicit cocyle
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