# Extending free group action on surfaces.

@article{Domnguez2020ExtendingFG, title={Extending free group action on surfaces.}, author={Jes{\'u}s Dom{\'i}nguez and Carlos Segovia}, journal={arXiv: Geometric Topology}, year={2020} }

The present work introduces new perspectives in order to extend finite group actions from surfaces to 3-manifolds. We consider the Schur multiplier associated to a finite group $G$ in terms of principal $G$-bordism in dimension two, called $G$-cobordism. We are interested in settle down the conjecture that every free action of a finite group on a closed oriented surface extends to a non-necessarily free action on a 3-manifold. We show this conjecture is true for abelian, dihedral, symmetric and…

## 3 Citations

### Free actions on surfaces that do not extend to arbitrary actions on 3-manifolds

- MathematicsComptes Rendus. Mathématique
- 2022

We provide the first known example of a finite group action on an oriented surface T that is free, orientation-preserving, and does not extend to an arbitrary (in particular, possibly non-free)…

### A T ] 4 N ov 2 02 1 ORIENTED AND UNITARY EQUIVARIANT BORDISM OF SURFACES

- Mathematics
- 2021

Fix a finite group G. We study Ω 2 and Ω 2 , the unitary and oriented bordism groups of smooth G-equivariant compact surfaces, respectively, with the restriction that in the oriented case G must have…

### Oriented and unitary equivariant bordism of surfaces

- Mathematics
- 2021

Fix a finite group G. We study Ω 2 and Ω 2 , the unitary and oriented bordism groups of smooth G-equivariant compact surfaces, respectively, with the restriction that in the oriented case G must have…

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