# Homotopy theory of the master equation package applied to algebra and geometry: a sketch of two interlocking programs

Banach Center Publications (2009)

- Volume: 85, Issue: 1, page 297-305
- ISSN: 0137-6934

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topDennis Sullivan. "Homotopy theory of the master equation package applied to algebra and geometry: a sketch of two interlocking programs." Banach Center Publications 85.1 (2009): 297-305. <http://eudml.org/doc/281675>.

@article{DennisSullivan2009,

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.},

author = {Dennis Sullivan},

journal = {Banach Center Publications},

keywords = {master equation; triangular free dgOa; free resolutions of dgOa; homotopy equivalence of dgOa maps; homotopy theory of general algebraic structures; quantum Lie bialgebras; minimal models for dgOa},

language = {eng},

number = {1},

pages = {297-305},

title = {Homotopy theory of the master equation package applied to algebra and geometry: a sketch of two interlocking programs},

url = {http://eudml.org/doc/281675},

volume = {85},

year = {2009},

}

TY - JOUR

AU - Dennis Sullivan

TI - Homotopy theory of the master equation package applied to algebra and geometry: a sketch of two interlocking programs

JO - Banach Center Publications

PY - 2009

VL - 85

IS - 1

SP - 297

EP - 305

AB - 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.

LA - eng

KW - master equation; triangular free dgOa; free resolutions of dgOa; homotopy equivalence of dgOa maps; homotopy theory of general algebraic structures; quantum Lie bialgebras; minimal models for dgOa

UR - http://eudml.org/doc/281675

ER -

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