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2017, Mathematical surveys and monographs, ISBN 9781470434823, Volume 217, 2 volumes
Book
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 classifying rational Poincaré duality spaces... 
Poincaré duality | 55U35 | 55S30 | Homotopy algebras | 55P62 | 18G55 | rational homotopy theory | MATHEMATICS | COHOMOLOGY | Poincare duality | POINCARE-DUALITY | A-INFINITY-ALGEBRAS
Journal Article
Journal of Homotopy and Related Structures, ISSN 2193-8407, 6/2016, Volume 11, Issue 2, pp. 261 - 289
... (Algebraic L-theory and topological nanifolds. Cambridge University Press, 1992) to the category of homotopy cosheaves of chain complexes of Ranicki and Weiss... 
Homotopy cosheaves | Algebraic Topology | L$$ L -theory | 19J25 | Mathematics | 19G24 | Total surgery obstruction | Rational Pontryagin classes | Algebra | Functional Analysis | 57R67 | Number Theory | 55U15 | L-theory | MATHEMATICS | DUALITY
Journal Article
1987, Lecture notes in mathematics, ISBN 0387136118, Volume 1264, viii, 219
This comprehensive monograph provides a self-contained treatment of the theory of I*-measure, or Sullivan's rational homotopy theory, from a constructive point of view... 
Measure theory | Homotopy theory | Differential algebra | Algebraic topology
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
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 construction... 
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 algebra of "semi-algebraic differential forms... 
OPERADS | MATHEMATICS
Journal Article
Algebra and Number Theory, ISSN 1937-0652, 2015, Volume 9, Issue 4, pp. 815 - 873
It is possible to talk about the etale homotopy equivalence of rational points on algebraic varieties by using a relative version of the etale homotopy type... 
Rational points | Étale homotopy | etale homotopy | MATHEMATICS | CHATELET SURFACES | BRAUER-MANIN OBSTRUCTION | rational points | COMPONENTS | 2 QUADRICS | CURVES | INTERSECTIONS | Mathematics - Number Theory
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
Journal of Homotopy and Related Structures, ISSN 2193-8407, 6/2016, Volume 11, Issue 2, pp. 309 - 332
Journal Article
Publications of the Research Institute for Mathematical Sciences, ISSN 0034-5318, 2016, Volume 52, Issue 3, pp. 297 - 308
We study the homotopy type of the space of all monic polynomials of degree d in C... 
Simplicial resolution | Homotopy type | Vassiliev spectral sequence | TOPOLOGY | MATHEMATICS | homotopy type | simplicial resolution | MAPS | RATIONAL FUNCTIONS
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
Rendiconti del Seminario Matematico dell 'Universita' di Padova/Mathematical Journal of the University of Padova, ISSN 0041-8994, 2017, Volume 138, pp. 209 - 221
Journal Article
Revista Matemática Complutense, ISSN 1139-1138, 7/2013, Volume 26, Issue 2, pp. 573 - 588
In this paper we describe explicit $$L_\infty $$ algebras modeling the rational homotopy type of any component of the spaces $$\text{ map}(X,Y)$$ and $$\text{ map}^*(X,Y... 
Rational homotopy theory | 54C35 | 55P62 | Mathematics | Topology | L_\infty $$ algebra | Geometry | Algebra | Mapping space | Analysis | Mathematics, general | Applications of Mathematics | L_\infty $$ model of a space | L∞ algebra | L∞ model of a space
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 of Knot Theory and Its Ramifications, ISSN 0218-2165, 04/2014, Volume 23, Issue 4, pp. 1450018 - 1-1450018-23
Arone and Turchin defined graph-complexes computing the rational homotopy of the spaces of long embeddings... 
Graph-complexes | Long embeddings | Rational homotopy | MATHEMATICS | rational homotopy | long embeddings | Homology | Graphs | Knot theory | Computation
Journal Article
Journal Article
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