Jean Morlet Chair - Trisections and related topics / Chaire Jean Morlet - Trisections et interactions

Collection Jean Morlet Chair - Trisections and related topics / Chaire Jean Morlet - Trisections et interactions

Organizer(s) Gay, David ; Moussard, Delphine

Date(s) 13/10/2025 - 17/10/2025

linked URL https://conferences.cirm-math.fr/3298.html

00:00:00 / 00:00:00

3 4

Equivariant trisections for group actions on four-manifolds

By Jeffrey Meier

Let G be a finite group, and let X be a smooth, orientable, connected, closed 4--dimensional G-manifold. Let S be a smooth, embedded, G-invariant surface in X. We will introduce the concept of a G-equivariant trisection of X and the notion of G-equivariant bridge trisected position for S. The main result is that any such X admits a G-equivariant trisection such that S is in equivariant bridge trisected position. The theory is designed so that G-equivariant (bridge) trisections are determined by their spines hence, the 4--dimensional equivariant topology of a G-manifold pair (X,S) can be reduced to the 2-dimensional data of a G-invariant shadow diagram. To achieve this, we prove an equivariant version of a theorem of Laudenbach and Poénaru. This talk is based on joint work with Evan Scott.

Information about the video

Date of recording 14/10/2025
Date of publication 30/10/2025
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers, Graduate Students
Director(s) Guillaume Hennenfent
Format MP4

Citation data

DOI 10.24350/CIRM.V.20395603
Cite this video Meier, Jeffrey (14/10/2025). Equivariant trisections for group actions on four-manifolds. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.20395603
URL https://dx.doi.org/10.24350/CIRM.V.20395603

Domain(s)

Geometric Topology

Bibliography

MEIER, Jeffrey et SCOTT, Evan. Equivariant trisections for group actions on four-manifolds. arXiv preprint arXiv:2501.17999, 2025. - https://doi.org/10.48550/arXiv.2501.17999
MEIER, Jeffrey et SCOTT, Evan. An equivariant Laudenbach-Poénaru theorem. arXiv preprint arXiv:2501.10524, 2025. - https://doi.org/10.48550/arXiv.2501.10524

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