Invariants of ℤ/p-homology 3-spheres from the abelianization of the level-p mapping class group

Wolfgang Pitsch, Ricard Riba

Producció científica: Contribució a revistaArticleRecercaAvaluat per experts

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 originalAnglès
Pàgines (de-a)1-85
Nombre de pàgines85
RevistaQuantum Topology
Volum15
Número1
DOIs
Estat de la publicacióPublicada - 17 de nov. 2023

Fingerprint

Navegar pels temes de recerca de 'Invariants of ℤ/p-homology 3-spheres from the abelianization of the level-p mapping class group'. Junts formen un fingerprint únic.

Com citar-ho