Johnson homomorphisms

DOI10.4171/EMSS/36zbMath1461.57004arXiv1909.03914OpenAlexW4206931039MaRDI QIDQ2656614

Richard M. Hain

Publication date: 11 March 2021

Published in: EMS Surveys in Mathematical Sciences (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1909.03914

zbMATH Keywords

surveymapping class groupTorelli groupJohnson homomorphismGoldman bracketTuraev cobracketmixed Hodge structure

Mathematics Subject Classification ID

Lie bialgebras; Lie coalgebras (17B62) Transcendental methods, Hodge theory (algebro-geometric aspects) (14C30) Topological properties of groups of homeomorphisms or diffeomorphisms (57S05) Research exposition (monographs, survey articles) pertaining to manifolds and cell complexes (57-02) 2-dimensional topology (including mapping class groups of surfaces, Teichmüller theory, curve complexes, etc.) (57K20)

Related Items

Hodge theory of the Turaev cobracket and the Kashiwara-Vergne problem, On the Torelli Lie algebra, Unnamed Item, A comparison of classes in the Johnson cokernels of the mapping class groups of surfaces

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The Kashiwara-Vergne conjecture and Drinfeld's associators
• Mixed Tate motives over \(\mathbb{Z}\)
• Variation of mixed Hodge structure. I
• Modules de Hodge polarisables. (Polarisable Hodge modules)
• On the derivation algebra of the free Lie algebra and trace maps
• Concomitants of ternary quartics and vector-valued Siegel and Teichmüller modular forms of genus three
• The structure of the Torelli group. I: A finite set of generators for \({\mathcal I}\)
• Noncommutative geometry and quiver algebras
• The structure of the Torelli group. II: A characterization of the group generated by twists on bounding curves
• The structure of the Torelli group. III: The abelianization of \({\mathcal S}\)
• Invariant functions on Lie groups and Hamiltonian flows of surface group representations
• The de Rham homotopy theory of complex algebraic varieties. I
• The Torelli groups for genus 2 and 3 surfaces
• On the intersection ring of compact three manifolds
• Extension of \(C^\infty\) function algebra by integrals and Malcev completion of \(\pi_1\)
• The algebraic topology of smooth algebraic varieties
• An abelian quotient of the mapping class group \(\mathfrak S\)
• Abelian quotients of subgroups of the mapping class group of surfaces
• Koszul DG-algebras arising from configuration spaces
• Stability of Schur functors
• Finite type 3-manifold invariants, the mapping class group and blinks
• Combinatorial Lie bialgebras of curves on surfaces.
• On a subgroup of the Grothendieck-Teichmüller group acting on the tower of profinite Teichmüller modular groups.
• On finiteness properties of the Johnson filtrations
• The Goldman-Turaev Lie bialgebra in genus zero and the Kashiwara-Vergne problem
• Representation stability for filtrations of Torelli groups
• Addendum and correction to: ``Homology cylinders: an enlargement of the mapping class group
• The rational cohomology ring of the moduli space of abelian 3-folds.
• Generators for the tautological algebra of the moduli space of curves.
• On a theorem of Kontsevich
• The modified diagonal cycle on the triple product of a pointed curve
• On some derivations of Lie algebras related to Galois representations
• Arithmetic group symmetry and finiteness properties of Torelli groups
• Hodge theory of the Goldman bracket
• The logarithms of Dehn twists
• A comparison of classes in the Johnson cokernels of the mapping class groups of surfaces
• Cohomology of local systems on the moduli of principally polarized abelian surfaces
• The Johnson cokernel and the Enomoto-Satoh invariant
• Representation theory and homological stability.
• New series in the Johnson cokernels of the mapping class groups of surfaces.
• Elliptic associators
• The stable moduli space of Riemann surfaces: Mumford's conjecture
• Structure of symplectic invariant Lie subalgebras of symplectic derivation Lie algebras
• Homology and central series of groups
• Théoreme de Lefschetz et critères de dégénérescence de suites spectrales
• Rational homotopy theory
• Théorie de Hodge. II. (Hodge theory. II)
• Théorie de Hodge. III
• The Hodge-de~Rham Theory of Modular Groups
• Rational points of universal curves
• Groupes fondamentaux motiviques de Tate mixte
• Braid monodromies on proper curves and pro-ℓ Galois representations
• A survey of the Torelli group
• The dimension of the Torelli group
• Relative Weight Filtrations on Completions of Mapping Class Groups
• On the holonomy Lie algebra and the nilpotent completion of the fundamental group of the complement of hypersurfaces
• Skein quantization of Poisson algebras of loops on surfaces
• Knots, Groups and 3-Manifolds (AM-84)
• Completions of mapping class groups and the cycle $C - C^-$
• Infinitesimal presentations of the Torelli groups
• The Second Cohomology with Symplectic Coefficients of the Moduli Space of Smooth Projective Curves
• Mapping Class Groups and Moduli Spaces of Curves
• The hodge de rham theory of relative malcev completion1
• Deligne-Beilinson Cohomology of Affine Groups
• Stable cohomology of the mapping class group with symplectic coefficients and of the universal Abel-Jacobi map
• Torelli Groups and Geometry of Moduli Spaces of Curves
• The mapping class group orbits in the framings of compact surfaces
• ON THE COHOMOLOGY OF TORELLI GROUPS
• UNIVERSAL MIXED ELLIPTIC MOTIVES
• Borel's stable range for the cohomology of arithmetic groups
• Genus 3 mapping class groups are not Kähler
• GALOIS ACTIONS ON FUNDAMENTAL GROUPS OF CURVES AND THE CYCLE $C-C^{-}$
• On the Automorphisms of Free Groups and Free Nilpotent Groups
• Automorphisms of a Class of Metabelian Groups
• Homological infiniteness of Torelli groups
• The primary approximation to the cohomology of the moduli space of curves and cocycles for the stable characteristic classes
• Intersection of curves on surfaces and their applications to mapping class groups