Homotopy groups of highly connected manifolds

DOI10.1016/j.aim.2018.08.006zbMath1433.55005arXiv1510.05195OpenAlexW2963282530WikidataQ129302483 ScholiaQ129302483MaRDI QIDQ1785790

Samik Basu, Somnath Basu

Publication date: 1 October 2018

Published in: Advances in Mathematics, International Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1510.05195

zbMATH Keywords

quadratic algebraloop spacefree loop spaceKoszul dualityhomotopy groupsperiodic geodesicsMoore conjecturerationally hyperbolic

Mathematics Subject Classification ID

Rational homotopy theory (55P62) Loop spaces (55P35) Geodesics in global differential geometry (53C22) Variational problems in applications to the theory of geodesics (problems in one independent variable) (58E10) Algebraic topology of manifolds (57N65) Homotopy groups of special spaces (55Q52) Stable homotopy groups (55Q10) Quadratic and Koszul algebras (16S37) Spectral sequences and homology of fiber spaces in algebraic topology (55R20)

Related Items (11)

The free loop space homology of \((n-1)\)-connected \(2n\)-manifolds ⋮ Loop space decompositions of \((2n-2)\)-connected \((4n-1)\)-dimensional Poincaré duality complexes ⋮ Loop homotopy of 6-manifolds over 4-manifolds ⋮ The rational homology ring of the based loop space of the gauge groups and the spaces of connections on a four-manifold ⋮ Suspension homotopy of 6-manifolds ⋮ Free loop space homology of highly connected manifolds ⋮ The loop space homotopy type of simply-connected four-manifolds and their generalizations ⋮ Homotopy groups of certain highly connected manifolds via loop space homology ⋮ Homotopy groups of highly connected manifolds ⋮ Algebraic topology in India ⋮ Homotopy groups of highly connected Poincaré duality complexes

Cites Work

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• On the chain algebra of a loop space
• The suspension triad of a sphere
• On manifolds homeomorphic to the 7-sphere
• On the structure of 5-manifolds
• The Sullivan conjecture on maps from classifying spaces
• The index growth and multiplicity of closed geodesics
• 8-manifolds admitting no differentiable structure
• Homotopical effects of dilatation
• Closed geodesics and the fundamental group
• On the number of closed geodesics on a compact Riemannian manifold
• Geodesics on \(S^ 2\) and periodic points of annulus homeomorphisms
• The diamond lemma for ring theory
• Existence of infinitely many closed geodesics
• The homology theory of the closed geodesic problem
• Formal and coformal spaces
• Torsion in homotopy groups
• On a generic property of geodesic flows
• Free loop space homology of highly connected manifolds
• Homotopy groups of highly connected manifolds
• On the growth rate of leaf-wise intersections
• The loop space homotopy type of simply-connected four-manifolds and their generalizations
• Homological stability of diffeomorphism groups
• On the structure of Hopf algebras
• The homotopy groups of Lie groups of low rank
• Periodic geodesics on compact Riemannian manifolds
• \(H\)-spaces from a homotopy point of view
• Circle bundles over 4-manifolds
• Homologie singulière des espaces fibrés. Applications
• Positive topological entropy of Reeb flows on spherizations
• THE BETTI NUMBERS OF THE FREE LOOP SPACE OF A CONNECTED SUM
• ON THE COBAR CONSTRUCTION
• Multiplication on Spheres (II)
• Loop Spaces of Finite Complexes at Large Primes
• A Remark on the Birkhoff-Witt Theorem
• Foundational Essays on Topological Manifolds, Smoothings, and Triangulations. (AM-88)
• Standard Lyndon Bases of Lie Algebras and Enveloping Algebras
• ON THE EXISTENCE OF CLOSED GEODESICS ON TWO-SPHERES
• On Simply-Connected 4-Manifolds
• Homotopy Associativity of H-Spaces. I
• A Connection Between the Whitehead and the Pontryagin Product
• ON THE HOMOTOPY GROUPS OF CERTAIN PAIRS AND TRIADS
• On the Homotopy Groups of the Union of Spheres
• Algebraic Operads
• On the Betti numbers of the free loop space of a coformal space

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