For a compact orientable surface of genus with one boundary component and for an odd prime number p, we study the homology of the unordered configuration spaces C. / n 0 Cn / with coefficients in Fp. We describe H.C. g;1/I Fp/ as a bigraded module over the Pontryagin ring H.C.D/I Fp/, where D is a disc, and compute in particular the bigraded dimension over Fp. We also consider the action of the mapping class group and prove that the mod-p Johnson kernelK. p/ is the kernel of the action on H.C. I F .
Bianchi, A., Stavrou, A. (2024). Homology of configuration spaces of surfaces modulo an odd prime. JOURNAL FÜR DIE REINE UND ANGEWANDTE MATHEMATIK, 0(0), 197-258 [10.1515/crelle-2024-0029].
Homology of configuration spaces of surfaces modulo an odd prime
Bianchi, Andrea;
2024
Abstract
For a compact orientable surface of genus with one boundary component and for an odd prime number p, we study the homology of the unordered configuration spaces C. / n 0 Cn / with coefficients in Fp. We describe H.C. g;1/I Fp/ as a bigraded module over the Pontryagin ring H.C.D/I Fp/, where D is a disc, and compute in particular the bigraded dimension over Fp. We also consider the action of the mapping class group and prove that the mod-p Johnson kernelK. p/ is the kernel of the action on H.C. I F .I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
