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math.GT2026
Image of the third Johnson homomorphism
Quentin Faes, Ricard Riba
In this note we show that the image of the third Johnson homomorphism coincides with the kernel of Morita's trace map for the case of a surface of genus with one boundary…
math.GT2025
A Parametrization of Integral Homology 3-Spheres by the Fourth Johnson subgroup
Ricard Riba
By results of Morita, Pitsch and, more recently, Faes, it is known that any integral homology 3-sphere can be constructed as a Heegaard splitting with a gluing map an element of th…
math.GT2023
Finite type invariants in low degrees and the Johnson filtration
Wolfgang Pitsch, Ricard Riba
We study the behaviour of the Casson invariant , its square, and Othsuki's second invariant as functions on the Johnson subgroup of the mapping class group. We show that s…