# 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} }

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

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