Letters in Mathematical Physics

, Volume 103, Issue 1, pp 79–112 | Cite as

Combinatorics and Formal Geometry of the Maurer–Cartan Equation

  • Joseph ChuangEmail author
  • Andrey Lazarev


We give a general treatment of the Maurer–Cartan equation in homotopy algebras and describe the operads and formal differential geometric objects governing the corresponding algebraic structures. We show that the notion of Maurer–Cartan twisting is encoded in certain automorphisms of these universal objects.

Mathematics Subject Classification (1991)

18D50 17B55 17B66 16E45 


differential graded Lie algebra Maurer–Cartan element A-infinity algebra L-infinity algebra operad twisting 


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Copyright information

© Springer Science+Business Media Dordrecht 2012

Authors and Affiliations

  1. 1.Centre for Mathematical ScienceCity University LondonLondonUK
  2. 2.Department of MathematicsUniversity of LeicesterLeicesterUK

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