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We prove that the first complex homology of the Johnson subgroup of the Torelli group $T_{g}$ is a non-trivial, unipotent $T_{g}$ -module for all $g \geq 4$ and give an explicit presentation of it as a $S y m_{.} H_{1} (T_{g}, C)$ -module when $g \geq 6$ . We do this by proving that, for a finitely generated group $G$ satisfying an assumption close to formality, the triviality of the restricted characteristic variety implies that the first homology of its Johnson kernel is a nilpotent module over the corresponding Laurent polynomial ring, isomorphic to the...

The boundary-Wecken classification of surfaces.

Brown, Robert F., Kelly, Michael R. (2004)

Algebraic & Geometric Topology

The Characteristic Toric Splitting of Irreducible Compact 3-Orbifolds.

F. Bonahon, L.C. Siebenmann (1987)

Mathematische Annalen

The Classification of Maps of Nonorietable Surfaces.

David Gabai, William H. Kazez (1988)

Mathematische Annalen

The classiflcation of maps of surfaces.

D. Gabai, W.H. Kazez (1987)

Inventiones mathematicae

The Degree of a Map Between Surfaces.

Richard Skora (1986)

Mathematische Annalen

The Dynamical Complexity of Orientation Reversing Homeomorphisms of Surfaces.

John Franks, Paul Blanchard (1980/1981)

Inventiones mathematicae

The extension of Johnson's homomorphism form the Torelli group to the mapping class group.

Shigeyuki Morita (1993)

Inventiones mathematicae

The fundamental groups of subsets of closed surfaces inject into their first shape groups.

Fischer, Hanspeter, Zastrow, Andreas (2005)

Algebraic & Geometric Topology

The genus of PSl2 (q).

Denis Sjerve, Henry Glover (1987)

Journal für die reine und angewandte Mathematik

The homotopy dimension of codiscrete subsets of the 2-sphere 𝕊²

J. W. Cannon, G. R. Conner (2007)

Fundamenta Mathematicae

Andreas Zastrow conjectured, and Cannon-Conner-Zastrow proved, that filling one hole in the Sierpiński curve with a disk results in a planar Peano continuum that is not homotopy equivalent to a 1-dimensional set. Zastrow's example is the motivation for this paper, where we characterize those planar Peano continua that are homotopy equivalent to 1-dimensional sets. While many planar Peano continua are not homotopy equivalent to 1-dimensional compacta, we prove that each has fundamental group that...

The Kazhdan property of the mapping class group of closed surfaces and the first cohomology group of its cofinite subgroups.

Taherkhani, Feraydoun (2000)

Experimental Mathematics

The Second Homology Group of the Mapping Class Group of an Orientable Surface.

John Harer (1983)

Inventiones mathematicae

The virtual cohomological dimension of the mapping class group of an orientable surface.

J.L. Harer (1986)

Inventiones mathematicae

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