INSTITUTE OF MATHEMATICS · POLISH ACADEMY OF SCIENCES
BANACH CENTER
PUBLICATIONS
ISSN: 0137-6934(p) 1730-6299(e)
Homotopy theory of the master equation package applied to algebra and geometry: a sketch of two interlocking programs
Dennis Sullivan1 Banach Center Publ. 85 (2009), 297-305
doi:10.4064/bc85-0-20 Abstract: Using the algebraic theory of homotopies between
maps of dga's we obtain a homotopy theory for algebraic structures
defined by collections of multiplications and comultiplications.
This is done by expressing these structures and resolved versions
of them in terms of dga maps. This same homotopy theory of dga maps
applies to extract invariants beyond
homological periods from systems of moduli spaces that determine
systems of chains that satisfy master equations
like $dX + X*X = 0$. Minimal models of these objects resemble
Postnikov decompositions in the homotopy theory of spaces and
maps.
