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Mat. Sb., 2000, Volume 191, Number 8, Pages 3–44 (Mi msb497)  

This article is cited in 14 scientific papers (total in 14 papers)

Massey products in symplectic manifolds

I. K. Babenkoa, I. A. Taimanovb

a M. V. Lomonosov Moscow State University
b Institute of Mathematics, Siberian Branch of USSR Academy of Sciences

Abstract: Massey products in symplectic manifolds are studied. A general method for the construction of symplectic manifolds with non-trivial Massey products of arbitrarily high order is put forward. This method uses symplectic blow-up. The authors find conditions guaranteeing that the symplectic blow-up of $X$ along a submanifold $Y$ inherits non-trivial Massey products from $X$ and $Y$. As a result, a general construction of non-formal symplectic manifolds by means of symplectic blow-ups is developed.


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English version:
Sbornik: Mathematics, 2000, 191:8, 1107–1146

Bibliographic databases:

UDC: 512.77
MSC: 55S30, 53C15
Received: 14.12.1999

Citation: I. K. Babenko, I. A. Taimanov, “Massey products in symplectic manifolds”, Mat. Sb., 191:8 (2000), 3–44; Sb. Math., 191:8 (2000), 1107–1146

Citation in format AMSBIB
\by I.~K.~Babenko, I.~A.~Taimanov
\paper Massey products in symplectic manifolds
\jour Mat. Sb.
\yr 2000
\vol 191
\issue 8
\pages 3--44
\jour Sb. Math.
\yr 2000
\vol 191
\issue 8
\pages 1107--1146

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    This publication is cited in the following articles:
    1. Verbitsky M., “Coherent sheaves on generic compact tori”, Algebraic Structures and Moduli Spaces, Crm Proceedings & Lecture Notes, 38, 2004, 229–247  crossref  mathscinet  zmath  isi
    2. Cavalcanti, GR, “Formality of k-connected spaces in 4k+3 and 4k+4 dimensions”, Mathematical Proceedings of the Cambridge Philosophical Society, 141 (2006), 101  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus  scopus
    3. Cavalcanti, GR, “The Lefschetz property, formality and blowing up in symplectic geometry”, Transactions of the American Mathematical Society, 359:1 (2007), 333  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    4. Verbitsky, M, “Coherent sheaves on general k3 surfaces and tori”, Pure and Applied Mathematics Quarterly, 4:3 (2008), 651  crossref  mathscinet  zmath  isi
    5. Cavalcanti G.R., Fernandez M., Munoz V., “On non-formality of a simply-connected symplectic 8-manifold”, Geometry and Physics XVI International Fall Workshop, Aip Conference Proceedings, 1023, 2008, 82–92  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus  scopus
    6. Vasiliy Dolgushev, Dmitry Tamarkin, Boris Tsygan, “Formality Theorems for Hochschild Complexes and Their Applications”, Lett Math Phys, 2009  crossref  mathscinet  isi  scopus  scopus  scopus
    7. D. V. Millionshchikov, “Algebra of Formal Vector Fields on the Line and Buchstaber's Conjecture”, Funct. Anal. Appl., 43:4 (2009), 264–278  mathnet  crossref  crossref  mathscinet  zmath  isi
    8. Misha Verbitsky, “Manifolds with parallel differential forms and Kähler identities for G2G2-manifolds”, Journal of Geometry and Physics, 61:6 (2011), 1001  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    9. I. K. Babenko, “Algebra, geometry, and topology of the substitution group of formal power series”, Russian Math. Surveys, 68:1 (2013), 1–68  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    10. Efrat I., “Single-Valued Massey Products”, Commun. Algebr., 42:11 (2014), 4609–4618  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    11. Lida Mendoza, E.G.. Reyes, “Massey products,A∞-algebras, differential equations, and Chekanov homology”, Journal of Nonlinear Mathematical Physics, 22:3 (2015), 342  crossref  mathscinet  scopus  scopus  scopus
    12. Biswas I., Fernandez M., Munoz V., Tralle A., “On formality of Sasakian manifolds”, J. Topol., 9:1 (2016), 161–180  crossref  mathscinet  zmath  isi  scopus
    13. Baues H.-J., Blanc D., Gondhali Sh., “Higher Toda brackets and Massey products”, J. Homotopy Relat. Struct., 11:4, SI (2016), 643–677  crossref  mathscinet  zmath  isi  scopus
    14. I. A. Taimanov, “Generalised Kummer construction and the cohomology rings of $G_2$-manifolds”, Sb. Math., 209:12 (2018), 1803–1811  mathnet  crossref  crossref  adsnasa  isi  elib
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