Homomorphic extensions of Johnson homomorphisms via Fox calculus

Bernard Perron

Displaying similar documents to “Homomorphic extensions of Johnson homomorphisms via Fox calculus”

Mapping class group and the Casson invariant

Bernard Perron (2004)

Annales de l’institut Fourier

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Using a new definition of the second and third Johsnon homomorphisms, we simplify and extend the work of Morita on the Casson invariant of homology-spheres defined by Heegard splittings. In particular, we calculate the Casson invariant of the homology-sphere obtained by gluing two handlebodies along a homeomorphism of the boundary belonging to the Torelli subgroup.

Partially defined cocycles and the Maslov index for a local ring

Amedeo Mazzoleni (2004)

Annales de l’institut Fourier

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In this paper we study some aspects of the cohomology of groups and we construct a central extension of the symplectic group $S p_{n} (A)$ .

Group Schemes over artinian rings and Applications

Ioan Berbec (2009)

Annales de l’institut Fourier

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Let $n$ be a positive integer and $A^{'}$ a complete characteristic zero discrete valuation ring with maximal ideal $𝔪$ , absolute ramification index $e < p - 1$ and perfect residue field $k$ of characteristic $p > 2$ . In this paper we classify smooth finite dimensional formal $p$ - groups over $A_{n}^{'} = A^{'} / 𝔪^{n} A^{'}$ , groups on which the “multiplication by $p$ ” morphism is faithfully flat, in particular $p$ -divisible groups. As applications, we prove that $p$ -divisible groups over $k$ , and the morphisms between them, lift canonically to $A^{'} / p A^{'}$ , and...

On component groups of Jacobians of Drinfeld modular curves

Mihran Papikian (2004)

Annales de l'Institut Fourier

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Let $J_{0} (𝔫)$ be the Jacobian variety of the Drinfeld modular curve $X_{0} (𝔫)$ over $𝔽_{q} (t)$ , where $𝔫$ is an ideal in $𝔽_{q} [t]$ . Let $0 \to B \to J_{0} (𝔫) \to A \to 0$ be an exact sequence of abelian varieties. Assume $B$ , as a subvariety of $J_{0} (𝔫)$ , is stable under the action of the Hecke algebra $𝕋 \subset$ End $(J_{0} (𝔫))$ . We give a criterion which is sufficient for the exactness of the induced sequence of component groups $0 \to Φ_{B, \infty} \to Φ_{J, \infty} \to Φ_{A, \infty} \to 0$ of the Néron models of these abelian varieties over $𝔽_{q} [[\frac{1}{t}]]$ . This criterion is always satisfied when either $A$ or $B$ is one-dimensional. Moreover, we prove that...