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- W4381245359 abstract "We study the relation between the set of oriented $mathbb{Z}/d$-homology $3$-spheres and the level-$d$ mapping class groups, the kernels of the canonical maps from the mapping class group of an oriented surface to the symplectic group with coefficients in $mathbb{Z}/dmathbb{Z}$. We formulate a criterion to decide whenever a $mathbb{Z}/d$-homology $3$-sphere can be constructed from a Heegaard splitting with gluing map an element of the level-$d$ mapping class group. Then we give a tool to construct invariants of $mathbb{Z}/d$-homology $3$-spheres from families of trivial $2$-cocycles on the level-$d$ mapping class groups. We apply this tool to find all the invariants of $mathbb{Z}/p$-homology $3$-spheres constructed from families of $2$-cocycles on the abelianization of the level-$p$ mapping class group with $p$ prime and to disprove the conjectured extension of the Casson invariant modulo a prime $p$ to rational homology $3$-spheres due B. Perron." @default.
- W4381245359 created "2023-06-20" @default.
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- W4381245359 date "2021-03-29" @default.
- W4381245359 modified "2023-10-16" @default.
- W4381245359 title "Invariants of $mathbb{Z}/p$-Homology 3-Spheres from the Abelianization of the Level-p Mapping Class Group" @default.
- W4381245359 doi "https://doi.org/10.48550/arxiv.2103.15519" @default.
- W4381245359 hasPublicationYear "2021" @default.
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