We 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.
Publié le :
DOI : 10.4171/RSMUP/6
DOI : 10.4171/RSMUP/6
Classification :
18, 32, 53
Mots-clés : Homotopy algebra, complex manifold, operad
Mots-clés : Homotopy algebra, complex manifold, operad
Affiliations des auteurs :
Bellier-Millès, Joan 1
@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}, publisher = {European Mathematical Society Publishing House}, address = {Zuerich, Switzerland}, volume = {140}, year = {2018}, doi = {10.4171/RSMUP/6}, mrnumber = {3880215}, zbl = {1419.18022}, url = {http://www.numdam.org/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://www.numdam.org/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://www.numdam.org/articles/10.4171/RSMUP/6/ %R 10.4171/RSMUP/6 %F RSMUP_2018__140__129_0
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. http://www.numdam.org/articles/10.4171/RSMUP/6/
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