Resum
We study the relation between the set of oriented 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 ℤ/dℤ. We formulate a criterion to decide whenever a 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 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 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 to B. Perron.
Idioma original | Anglès |
---|---|
Pàgines (de-a) | 1-85 |
Nombre de pàgines | 85 |
Revista | Quantum Topology |
Volum | 15 |
Número | 1 |
DOIs | |
Estat de la publicació | Publicada - 17 de nov. 2023 |