A note on the Nielsen realization problem for K3 surfaces
| dc.contributor.author | Baraglia, D. | |
| dc.contributor.author | Konno, H. | |
| dc.date.issued | 2023 | |
| dc.description.abstract | We will show the following three theorems on the diffeomorphism and homeomorphism groups of a K3 surface. The first theorem is that the natural map π₀ (Diff(K3)) → Aut(H²(K3;Z)) has a section over its image. The second is that there exists a subgroup G of π₀ (Diff(K3)) of order two over which there is no splitting of the map (Diff(K3) → π₀ (Diff(K3)), but there is a splitting of Homeo(K3) → π₀(Homeo(K3)) over the image of G in π₀(Homeo(K3)), which is non-trivial. The third is that the map π₁(Diff(K3)) → π₁(Homeo(K3)) is not surjective. Our proof of these results is based on Seiberg-Witten theory and the global Torelli theorem for K3 surfaces. | |
| dc.description.statementofresponsibility | David Baraglia and Hokuto Konno | |
| dc.identifier.citation | Proceedings of the American Mathematical Society, 2023; 151(9):4079-4087 | |
| dc.identifier.doi | 10.1090/proc/15544 | |
| dc.identifier.issn | 0002-9939 | |
| dc.identifier.issn | 1088-6826 | |
| dc.identifier.orcid | Baraglia, D. [0000-0002-8450-1165] | |
| dc.identifier.uri | https://hdl.handle.net/2440/139031 | |
| dc.language.iso | en | |
| dc.publisher | American Mathematical Society | |
| dc.relation.grant | http://purl.org/au-research/grants/arc/DP170101054 | |
| dc.rights | © 2023 American Mathematical Society | |
| dc.source.uri | https://doi.org/10.1090/proc/15544 | |
| dc.title | A note on the Nielsen realization problem for K3 surfaces | |
| dc.type | Journal article | |
| pubs.publication-status | Published |