Path components of $\mathrm{G}_2$-moduli spaces may be non-aspherical
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866909545255665664 |
|---|---|
| author | Crowley, Diarmuid Goette, Sebastian Hertl, Thorsten |
| author_facet | Crowley, Diarmuid Goette, Sebastian Hertl, Thorsten |
| contents | Starting from Joyce's generalised Kummer construction, we exhibit non-trivial families of $\mathrm{G}_2$-manifolds over the two dimensional sphere by resolving singularities with a twisted family of Eguchi-Hanson spaces. We establish that the comparison map $\mathcal{G}_2^{\mathrm{tf}}(M) /\!\!/ \mathrm{Diff}(M)_0 \rightarrow \mathcal{G}_2^{\mathrm{tf}}(M) / \mathrm{Diff}(M)_0$ is a fibration over each path components with Eilenberg Mac Lane spaces as fibres, which allows us to show that these families remain non-trivial in $\mathcal{G}_2^{\mathrm{tf}}(M) / \mathrm{Diff}(M)_0$. In addition, we construct a new invariant based on characteristic classes that allows us to show that different resolutions give rise to different elements in the moduli space. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_15829 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Path components of $\mathrm{G}_2$-moduli spaces may be non-aspherical Crowley, Diarmuid Goette, Sebastian Hertl, Thorsten Geometric Topology Differential Geometry 55Q52, 57R20 (Primary), 53C29, 57R20, 58D27 (Secondary) Starting from Joyce's generalised Kummer construction, we exhibit non-trivial families of $\mathrm{G}_2$-manifolds over the two dimensional sphere by resolving singularities with a twisted family of Eguchi-Hanson spaces. We establish that the comparison map $\mathcal{G}_2^{\mathrm{tf}}(M) /\!\!/ \mathrm{Diff}(M)_0 \rightarrow \mathcal{G}_2^{\mathrm{tf}}(M) / \mathrm{Diff}(M)_0$ is a fibration over each path components with Eilenberg Mac Lane spaces as fibres, which allows us to show that these families remain non-trivial in $\mathcal{G}_2^{\mathrm{tf}}(M) / \mathrm{Diff}(M)_0$. In addition, we construct a new invariant based on characteristic classes that allows us to show that different resolutions give rise to different elements in the moduli space. |
| title | Path components of $\mathrm{G}_2$-moduli spaces may be non-aspherical |
| topic | Geometric Topology Differential Geometry 55Q52, 57R20 (Primary), 53C29, 57R20, 58D27 (Secondary) |
| url | https://arxiv.org/abs/2503.15829 |