On the Extension of a TCFT to the Boundary of the Moduli Space

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The purpose of this paper is to describe an analogue of a construction of Costello in the context of finite-dimensional differential graded Frobenius algebras which produces closed forms on the decorated moduli space of Riemann surfaces. We show that this construction extends to a certain natural compactification of the moduli space which is associated with the modular closure of the associative operad, due to the absence of ultra-violet divergences in the finite-dimensional case. We demonstrate that this construction is equivalent to the "dual construction" of Kontsevich.

Original languageEnglish
Pages (from-to)111-132
Number of pages22
JournalLetters in Mathematical Physics
Issue number2
StatePublished - Nov 2011


  • modular operad
  • moduli spaces of curves
  • orbi-cell complexes
  • topological conformal field theory


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