• Corpus ID: 227306014

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… 

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References

SHOWING 1-10 OF 13 REFERENCES

Extending finite group actions from surfaces to handlebodies

We show that every action of a finite dihedral group on a closed orientable surface F extends to a 3-dimensional handlebody V , with ∂V = F . In the case of a finite abelian group G, we give

On Schottky Groups with Automorphisms

We consider a closed Riemann surface S and a group H of conformal automor-phisms of S. We seek a Schottky uniformization ((; G; : ! S) of the surface S with the property that every element of H can

Differentiable periodic maps

1. The bordism groups. This note presents an outline of the authors' efforts to apply Thorn's cobordism theory [ó] to the study of differentiable periodic maps. First, however, we shall outline our

G-Topological quantum field theory

In this expository paper, we give an explicit construction of an isomorphism between the category of homotopical quantum field theories with an underlying Eilenberg–MacLane space K(G, 1) and the

The second homology group of a group; relations among commutators

We are concerned with the problem of assigning a group theoretic interpretation to the second homology group H2(G, J) of a group G, with integer coefficients, J[l, p. 486]. We shall define a new

Topological quantum field theory

A twisted version of four dimensional supersymmetric gauge theory is formulated. The model, which refines a nonrelativistic treatment by Atiyah, appears to underlie many recent developments in

Cohomology of groups

  • L. Evens
  • Engineering
    Oxford mathematical monographs
  • 1991
A rink-type roller skate is provided with a plastic sole plate. To mount a toe stop on the skate, a novel bushing is embedded in the sole plate. The bushing has relatively small diameter ends and a

The Oxford University Press

An examination of the cult of Sainte Genevieve, the patron saint of Paris. Using hagiographical and liturgical documents, as well as municipal, ecclesiastical and notarial records, it analyzes the

The classifying space of the 1+1 dimensional G-cobordism category

The 1+1 G-cobordism category, with G a finite group, is important in the construction of G-topological field theories which are completely determined by a G-Frobenius algebra. We give a description

The Schur Multipler

  • 1987