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

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

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

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

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

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

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

OPERADS | MATHEMATICS

Journal Article

Journal of Homotopy and Related Structures, ISSN 2193-8407, 9/2017, Volume 12, Issue 3, pp. 691 - 706

Let $$\mathcal {E}(X)$$ E ( X ) be the group of homotopy classes of self homotopy equivalences for a connected CW complex X...

mathcal {E}$$ E -Map | Algebraic Topology | Rationally $$\mathcal {E}$$ E -equivalent | 55P62 | Mathematics | 55P10 | Algebra | Rational co- $$\mathcal {E}$$ E -map | Functional Analysis | Sullivan (minimal) model | Rational homotopy | Co- $$\mathcal {E}$$ E -map | Rational $$\mathcal {E}$$ E -map | Number Theory | Self homotopy equivalence | E-Map | Rational co-E-map | Rationally E-equivalent | Co-E-map | Rational E-map | MATHEMATICS | Co-epsilon-map | epsilon-Map | Rationally epsilon-equivalent | Rational epsilon-map | Rational co-epsilon-map

mathcal {E}$$ E -Map | Algebraic Topology | Rationally $$\mathcal {E}$$ E -equivalent | 55P62 | Mathematics | 55P10 | Algebra | Rational co- $$\mathcal {E}$$ E -map | Functional Analysis | Sullivan (minimal) model | Rational homotopy | Co- $$\mathcal {E}$$ E -map | Rational $$\mathcal {E}$$ E -map | Number Theory | Self homotopy equivalence | E-Map | Rational co-E-map | Rationally E-equivalent | Co-E-map | Rational E-map | MATHEMATICS | Co-epsilon-map | epsilon-Map | Rationally epsilon-equivalent | Rational epsilon-map | Rational co-epsilon-map

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

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

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

By using homotopy transfer techniques in the context of rational homotopy theory, we show that if $$C...

Algebra | L_\infty $$ L ∞ -algebra | Functional Analysis | Mapping space | Secondary 54C35 | Algebraic Topology | Rational homotopy | Mathematics | Number Theory | Primary 55P62 | algebra | MATHEMATICS | L-infinity-algebra | LIE-ALGEBRA | Mathematics - Algebraic Topology

Algebra | L_\infty $$ L ∞ -algebra | Functional Analysis | Mapping space | Secondary 54C35 | Algebraic Topology | Rational homotopy | Mathematics | Number Theory | Primary 55P62 | algebra | MATHEMATICS | L-infinity-algebra | LIE-ALGEBRA | Mathematics - Algebraic Topology

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

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

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

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

Our main purpose in this paper is to resolve, in a rational homotopy theory context, the following open question asked by S. Theriaul...

Lie derivation | Rational homotopy theory | Sullivanminimalmodels | Homotopical nilpotency | Self homotopy equivalences | Quillenminimalmodels | Cocategory | Classifying space | MATHEMATICS | Sullivan minimal models | MATHEMATICS, APPLIED | classifying space | Quillen minimal models | NILPOTENT GROUPS | homotopical nilpotency | SPACES | self homotopy equivalences | cocategory

Lie derivation | Rational homotopy theory | Sullivanminimalmodels | Homotopical nilpotency | Self homotopy equivalences | Quillenminimalmodels | Cocategory | Classifying space | MATHEMATICS | Sullivan minimal models | MATHEMATICS, APPLIED | classifying space | Quillen minimal models | NILPOTENT GROUPS | homotopical nilpotency | SPACES | self homotopy equivalences | cocategory

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

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

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

Graph-complexes | Long embeddings | Rational homotopy | MATHEMATICS | rational homotopy | long embeddings | Homology | Graphs | Knot theory | Computation

Journal Article

Russian Mathematical Surveys, ISSN 0036-0279, 2016, Volume 71, Issue 2, pp. 185 - 251

.... 1 surveys some of the main results in the homotopy theory of these spaces. Chap. 2 breaks new ground by initiating a study of the map (w) over tilde...

Higher whitehead product | Higher samelson product | Davis-Januszkiewicz space | Moment-angle complex | Polyhedral product | Homotopy type | homotopy type | TORUS ACTIONS | COMPLEXES | higher Samelson product | MOMENT-ANGLE MANIFOLDS | POLYHEDRAL PRODUCT FUNCTOR | RATIONAL HOMOTOPY | MATHEMATICS | moment-angle complex | higher Whitehead product | STANLEY-REISNER RINGS | CONNECTED-SUMS | polyhedral product | CONVEX POLYTOPES | COORDINATE SUBSPACE ARRANGEMENT | SIMPLICIAL POSETS | Algebra | Homotopy theory | Mathematical analysis | Texts | Grounds | Topology | Formulas (mathematics) | Combinatorial analysis

Higher whitehead product | Higher samelson product | Davis-Januszkiewicz space | Moment-angle complex | Polyhedral product | Homotopy type | homotopy type | TORUS ACTIONS | COMPLEXES | higher Samelson product | MOMENT-ANGLE MANIFOLDS | POLYHEDRAL PRODUCT FUNCTOR | RATIONAL HOMOTOPY | MATHEMATICS | moment-angle complex | higher Whitehead product | STANLEY-REISNER RINGS | CONNECTED-SUMS | polyhedral product | CONVEX POLYTOPES | COORDINATE SUBSPACE ARRANGEMENT | SIMPLICIAL POSETS | Algebra | Homotopy theory | Mathematical analysis | Texts | Grounds | Topology | Formulas (mathematics) | Combinatorial analysis

Journal Article

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