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The Breadth of Symplectic and Poisson Geometry pp 583–601Cite as

Poisson homotopy algebra: An idiosyncratic survey of homotopy algebraic topics related to Alan’s interests

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Part of the book series: Progress in Mathematics ((PM,volume 232))

Abstract

Homotopy algebra is playing an increasing role in mathematical physics. Especially in the Hamiltonian and Lagrangian settings, it is intimately related to some of Alan’s interests, e.g., Courant and Lie algebroids. There is a comparatively long history of such structure in cohomological physics in terms of equations that hold mod exact terms (typically, divergences) or only “on shell,” meaning modulo the Euler—Lagrange equations of “motion”; more recently, higher homotopies have come into prominence. Higher homotopies were developed first within algebraic topology and may not yet be commonly available tools for symplectic geometers and mathematical physicists.

This is an expanded version of my talk at Alanfest, planned as a gentle introduction to the basic point of view with a variety of applications to substantiate its relevance. Most technical details are supplied by references to the original work or to [MSS02].

This research was supported in part by NSF Focussed Research Grant DMS 0139799.

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of North Carolina, Chapel Hill, NC, 27599, USA

    Jim Stasheff

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  1. Jim Stasheff
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Editors and Affiliations

  1. Department of Engineering and Applied Science Control and Dynamical Systems, California Institute of Technology, Pasadena, CA, 91125, USA

    Jerrold E. Marsden

  2. Département de Mathématiques, Ecole Polytechnique Fédérale de Lausanne, CH-1015, Lausanne, Switzerland

    Tudor S. Ratiu

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Dedicated to Alan Weinstein on his 60th birthday.

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Stasheff, J. (2005). Poisson homotopy algebra: An idiosyncratic survey of homotopy algebraic topics related to Alan’s interests. In: Marsden, J.E., Ratiu, T.S. (eds) The Breadth of Symplectic and Poisson Geometry. Progress in Mathematics, vol 232. Birkhäuser Boston. https://doi.org/10.1007/0-8176-4419-9_20

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