EXTENSIONS OF JOHNSON'S AND MORITA'S HOMOMORPHISMS THAT MAP TO FINITELY GENERATED ABELIAN GROUPS

DOI10.1142/S1793525313500027zbMath1270.57006arXiv0910.4777MaRDI QIDQ4916966

Matthew B. Day

Publication date: 26 April 2013

Published in: Journal of Topology and Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0910.4777

zbMATH Keywords

free groupmapping class groupJohnson homomorphismcrossed homomorphismautomorphism group of free groupnilpotent homogeneous space

Mathematics Subject Classification ID

Geometric group theory (20F65) Topological methods in group theory (57M07)

Related Items

Canonical extensions of Morita homomorphisms to the Ptolemy groupoid, On the graded quotients of the \(\operatorname{SL}_m\)-representation algebras of groups, The logarithms of Dehn twists, On the SL(2, C)-representation rings of free abelian groups

Cites Work

• Extended flux maps on surfaces and the contracted Johnson homomorphism
• Canonical extensions of Morita homomorphisms to the Ptolemy groupoid
• Canonical extensions of the Johnson homomorphisms to the Torelli groupoid
• The extension of Johnson's homomorphism from the Torelli group to the mapping class group
• Infinitesimal computations in topology
• An abelian quotient of the mapping class group \(\mathfrak S\)
• Abelian quotients of subgroups of the mapping class group of surfaces
• Homomorphic extensions of Johnson homomorphims via Fox calculus.
• Extending Johnson's and Morita's homomorphisms to the mapping class group
• On the cohomology of compact homogeneous spaces of nilpotent Lie groups
• A survey of the Torelli group
• NEW OBSTRUCTIONS FOR THE SURJECTIVITY OF THE JOHNSON HOMOMORPHISM OF THE AUTOMORPHISM GROUP OF A FREE GROUP
• Torelli groups, extended Johnson homomorphisms, and new cycles on the moduli space of curves
• Infinitesimal presentations of the Torelli groups
• On the Automorphisms of Free Groups and Free Nilpotent Groups
• Links, pictures and the homology of nilpotent groups