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MR ZblWe prove an equivalence of categories from formal complex structures with formal holomorphic maps to homotopy algebras over a simple operad with its associated homotopy morphisms. We extend this equivalence to complex manifolds. A complex structure on a smooth manifold corresponds in this way to a family of algebras indexed by the points of the manifold.
DOI : 10.4171/RSMUP/6
Mots-clés : Homotopy algebra, complex manifold, operad
Bellier-Millès, Joan 1
Bellier-Millès, Joan. Complex manifolds as families of homotopy algebras. Rendiconti del Seminario Matematico della Università di Padova, Tome 140 (2018), pp. 129-172. doi: 10.4171/RSMUP/6
@article{RSMUP_2018__140__129_0,
author = {Bellier-Mill\`es, Joan},
title = {Complex manifolds as families of homotopy algebras},
journal = {Rendiconti del Seminario Matematico della Universit\`a di Padova},
pages = {129--172},
year = {2018},
publisher = {European Mathematical Society Publishing House},
address = {Zuerich, Switzerland},
volume = {140},
doi = {10.4171/RSMUP/6},
mrnumber = {3880215},
zbl = {1419.18022},
url = {http://geodesic.mathdoc.fr/articles/10.4171/RSMUP/6/}
}
TY - JOUR AU - Bellier-Millès, Joan TI - Complex manifolds as families of homotopy algebras JO - Rendiconti del Seminario Matematico della Università di Padova PY - 2018 SP - 129 EP - 172 VL - 140 PB - European Mathematical Society Publishing House PP - Zuerich, Switzerland UR - http://geodesic.mathdoc.fr/articles/10.4171/RSMUP/6/ DO - 10.4171/RSMUP/6 ID - RSMUP_2018__140__129_0 ER -
%0 Journal Article %A Bellier-Millès, Joan %T Complex manifolds as families of homotopy algebras %J Rendiconti del Seminario Matematico della Università di Padova %D 2018 %P 129-172 %V 140 %I European Mathematical Society Publishing House %C Zuerich, Switzerland %U http://geodesic.mathdoc.fr/articles/10.4171/RSMUP/6/ %R 10.4171/RSMUP/6 %F RSMUP_2018__140__129_0
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