The fixed-point property for simply connected plane continua

@article{Hagopian1996TheFP,
  title={The fixed-point property for simply connected plane continua},
  author={C. Hagopian},
  journal={Transactions of the American Mathematical Society},
  year={1996},
  volume={348},
  pages={4525-4548}
}
  • C. Hagopian
  • Published 1996
  • Mathematics
  • Transactions of the American Mathematical Society
We answer a question of R. Mańka by proving that every simplyconnected plane continuum has the fixed-point property. It follows that an arcwise-connected plane continuum has the fixed-point property if and only if its fundamental group is trivial. Let M be a plane continuum with the property that every simple closed curve in M bounds a disk in M . Then every map of M that sends each arc component into itself has a fixed point. Hence every deformation of M has a fixed point. These results are… Expand
13 Citations

Figures from this paper

...
1
2
...

References

SHOWING 1-10 OF 47 REFERENCES
Fixed points of arc-component-preserving maps
  • 8
  • PDF
Another fixed point theorem for plane continua
  • 13
  • PDF
On fixed point properties of plane continua
  • 43
  • PDF
A fixed point theorem for plane homeomorphisms
  • 25
  • PDF
Fixed-point theorems for arcwise connected continua
  • 33
  • PDF
Some fixed point theorems
  • 64
  • PDF
...
1
2
3
4
5
...