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2017, Mathematical surveys and monographs, ISBN 9781470434823, Volume 217, 2 volumes
Book
Advances in Mathematics, ISSN 0001-8708, 03/2013, Volume 236, pp. 60 - 91
We develop a homotopy theory of L∞ algebras based on the Lawrence–Sullivan construction, a complete differential graded Lie algebra which, as we show, satisfies the necessary properties to become the right cylinder in this category... 
Rational homotopy theory | [formula omitted]-algebras | Algebraic models of non-connected spaces | Maurer–Cartan set | algebras | Maurer-Cartan set | Analysis | Models | Algebra
Journal Article
Georgian Mathematical Journal, ISSN 1072-947X, 12/2018, Volume 25, Issue 4, pp. 493 - 512
In this paper, we set up a rational homotopy theory for operads in simplicial sets whose term of arity one is not necessarily reduced to an operadic unit, extending results obtained by the author in the book [B... 
55P62 | rational homotopy | 18D50 | Sullivan models | Operads | 18G55 | MATHEMATICS | Mathematics - Algebraic Topology
Journal Article
Georgian Mathematical Journal, ISSN 1072-947X, 12/2018, Volume 25, Issue 4, pp. 545 - 570
Kadeishvili proposes a minimal -algebra as a rational homotopy model of a space. We discuss a cyclic version of this Kadeishvili -model and apply it to... 
Poincaré duality | 55U35 | 55S30 | Homotopy algebras | 55P62 | 18G55 | rational homotopy theory | MATHEMATICS | COHOMOLOGY | Poincare duality | POINCARE-DUALITY | A-INFINITY-ALGEBRAS
Journal Article
Transactions of the American Mathematical Society, ISSN 0002-9947, 02/2013, Volume 365, Issue 2, pp. 861 - 883
We develop a new framework which resolves the homotopy periods problem. We start with integer-valued homotopy periods defined explicitly from the classic bar... 
Rational homotopy theory | Graph cohomology | Hopf invariants | Lie coalgebras | MATHEMATICS | rational homotopy theory | graph cohomology
Journal Article
Algebraic and Geometric Topology, ISSN 1472-2747, 2011, Volume 11, Issue 5, pp. 2477 - 2545
We complete the details of a theory outlined by Kontsevich and Soibelman that associates to a semi-algebraic set a certain graded commutative differential... 
OPERADS | MATHEMATICS
Journal Article
Advances in Mathematics, ISSN 0001-8708, 10/2015, Volume 283, pp. 303 - 361
We construct two algebraic versions of homotopy theory of rational disconnected topological spaces, one based on differential graded commutative associative algebras and the other one on complete... 
Rational homotopy theory | Maurer–Cartan simplicial set | Differential graded Lie algebra | Koszul duality | Closed model category | Maurer-Cartan simplicial set | MATHEMATICS | ALGEBRAS | Roszul duality | MODELS | Algebra
Journal Article
Mathematische Zeitschrift, ISSN 0025-5874, 8/2012, Volume 271, Issue 3, pp. 961 - 1010
This paper is a generalization of Moriya (in J Pure Appl Algebra 214(4): 422–439, 2010). We develop the de Rham homotopy theory of not necessarily nilpotent spaces... 
Rational homotopy theory | Mathematics, general | Mathematics | Schematic homotopy type | Non-simply connected space | Dg-category | MATHEMATICS
Journal Article
Fortschritte der Physik, ISSN 0015-8208, 2019, Volume 67, Issue 8-9, p. 1910003
We review a first-principles derivation of Type IIA D-brane charges from M-theory degrees of freedom in the approximation of super rational homotopy theory. 
Green–Schwarz sigma models | double dimensional reduction | M-branes | gauge enhancement | rational homotopy theory | parametrised homotopy theory | PHYSICS, MULTIDISCIPLINARY | Green-Schwarz sigma models | Conferences, meetings and seminars | Conferences and conventions | Analysis
Journal Article
Fortschritte der Physik, ISSN 0015-8208, 08/2019, Volume 67, Issue 8-9, p. n/a
We review a first‐principles derivation of Type IIA D‐brane charges from M‐theory degrees of freedom in the approximation of super rational homotopy theory... 
Green–Schwarz sigma models | double dimensional reduction | gauge enhancement | M‐branes | rational homotopy theory | parametrised homotopy theory
Journal Article
Journal Article
Homology, Homotopy and Applications, ISSN 1532-0073, 2011, Volume 13, Issue 2, pp. 263 - 292
We give a new presentation of the Lie cooperad as a quotient of the graph cooperad, a presentation which is not linearly dual to any of the standard... 
Rational homotopy theory | Lie coalgebras | Graph cohomology | MATHEMATICS | MATHEMATICS, APPLIED | ALGEBRA | rational homotopy theory | graph cohomology | 16E40 | 55P48 | 55P62
Journal Article
Journal of Mathematical Sciences, ISSN 1072-3374, 10/2019, Volume 242, Issue 3, pp. 413 - 426
.... This class is a natural generalization of the class of 1-connected spaces for which the rational homotopy theory was constructed in work [10... 
rational shape theory | Mathematics, general | Mathematics | Homotopy theory | theory of shape | rational homotopy theory
Journal Article
Canadian mathematical bulletin, ISSN 0008-4395, 06/2006, Volume 49, Issue 2, pp. 237 - 246
... ${{\mathbb{P}}^{m}}$ are approximated by rational mappings. The fundamental tool employed is homotopy theory. 
Rational approximation | Null-homotopic | Homotopy type | MATHEMATICS
Journal Article
1997, Lecture notes in mathematics, ISBN 9783540631057, Volume 1661., viii, 207
Book
Transactions of the American Mathematical Society, ISSN 0002-9947, 10/2009, Volume 361, Issue 10, pp. 5601 - 5614
We give an explicit Lie model for any component of the space of free and pointed sections of a nilpotent fibration, and in particular, of the free and pointed... 
Morphisms | Algebra | Mathematical theorems | Homotopy theory | Maps | Functors | Mathematical models | Vector space models | Vector spaces | Rational homotopy theory | Space of sections | Mapping space | Sullivan model | Quillen model | SPACE | MATHEMATICS | mapping space | RATIONAL HOMOTOPY-THEORY | rational homotopy theory
Journal Article
Homology, Homotopy and Applications, ISSN 1532-0073, 2016, Volume 18, Issue 2, pp. 303 - 336
We extend a construction of Hinich to obtain a closed model category structure on all differential graded cocommutative coalgebras over an algebraically closed... 
Coalgebra | Deformation | Curved Lie algebra | Rational homotopy | coalgebra | curved Lie algebra | OPERADS | MATHEMATICS | MODEL-CATEGORIES | MATHEMATICS, APPLIED | SPACES | deformation | rational homotopy
Journal Article
Algebraic and Geometric Topology, ISSN 1472-2747, 11/2016, Volume 16, Issue 5, pp. 2637 - 2661
To any graph and smooth algebraic curve C, one may associate a "hypercurve" arrangement, and one can study the rational homotopy theory of the complement X... 
Rational homotopy theory | Toric arrangement | Hyperplane arrangement | Elliptic arrangement | Koszul duality | TOPOLOGY | MATHEMATICS | COMPLEMENT | KOSZUL ALGEBRAS | SPACES | MODEL | HYPERPLANES | GRAPHS
Journal Article
Revista matemática complutense, ISSN 1988-2807, 2019, Volume 33, Issue 1, pp. 187 - 196
We prove that the (reduced) rational sectional category of the universal fibration with fibre X, for X any space that satisfies a well-known conjecture of... 
Rational homotopy theory | MATHEMATICS | MATHEMATICS, APPLIED | Universal fibration | Sectional category | Lusternik-Schnirelmann category | HOMOTOPY | Halperin conjecture
Journal Article
by Cao, J
HOMOLOGY HOMOTOPY AND APPLICATIONS, ISSN 1532-0073, 2019, Volume 21, Issue 2, pp. 145 - 169
In this paper, we study the general properties of commutative differential graded algebras in the category of representations over a reductive algebraic group... 
MATHEMATICS | MATHEMATICS, APPLIED | reductive group | Hopf algebra | rational homotopy theory | Tannakian category | graded differential algebra
Journal Article
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