Open Access. Powered by Scholars. Published by Universities.®
- Publication Type
Articles 1 - 6 of 6
Full-Text Articles in Mathematics
C^1 Actions Of The Mapping Class Group On The Circle, Kamlesh Parwani
C^1 Actions Of The Mapping Class Group On The Circle, Kamlesh Parwani
Kamlesh Parwani
Let S be a connected orientable surface with finitely many punctures, finitely many boundary components, and genus at least 6. Then any C^1 action of the mapping class group of S on the circle is trivial. The techniques used in the proof of this result permit us to show that products of Kazhdan groups and certain lattices cannot have C^1 faithful actions on the circle. We also prove that for n > 5, any C^1 action of Aut(F_n) or Out(F_n) on the circle factors through an action of Z/2Z.
The Two Variable Substitution Problem For Free Products Of Groups, Leo P. Comerford, Charles C. Edmunds
The Two Variable Substitution Problem For Free Products Of Groups, Leo P. Comerford, Charles C. Edmunds
Leo Comerford
We consider equations of the form W(x,y) = U with U an element of a free product G of groups. We show that with suitable algorithmic conditions on the free factors of G, one can effectively determine whether or not the equations have solutions in G. We also show that under certain hypotheses on the free factors of G and the equation itself, the equation W(x,y) = U has only finitely many solutions, up to the action of the stabilizer of W(x,y) in Aut().
The Two Variable Substitution Problem For Free Products Of Groups, Leo P. Comerford, Charles C. Edmunds
The Two Variable Substitution Problem For Free Products Of Groups, Leo P. Comerford, Charles C. Edmunds
Faculty Research and Creative Activity
We consider equations of the form W(x,y) = U with U an element of a free product G of groups. We show that with suitable algorithmic conditions on the free factors of G, one can effectively determine whether or not the equations have solutions in G. We also show that under certain hypotheses on the free factors of G and the equation itself, the equation W(x,y) = U has only finitely many solutions, up to the action of the stabilizer of W(x,y) in Aut().
C^1 Actions Of The Mapping Class Group On The Circle, Kamlesh Parwani
C^1 Actions Of The Mapping Class Group On The Circle, Kamlesh Parwani
Faculty Research and Creative Activity
Let S be a connected orientable surface with finitely many punctures, finitely many boundary components, and genus at least 6. Then any C^1 action of the mapping class group of S on the circle is trivial. The techniques used in the proof of this result permit us to show that products of Kazhdan groups and certain lattices cannot have C^1 faithful actions on the circle. We also prove that for n > 5, any C^1 action of Aut(F_n) or Out(F_n) on the circle factors through an action of Z/2Z.
The Two Variable Substitution Problem For Free Products Of Groups, Leo Comerford, Charles Edmunds
The Two Variable Substitution Problem For Free Products Of Groups, Leo Comerford, Charles Edmunds
Faculty Research and Creative Activity
We consider equations of the form W(x,y) = U with U an element of a free product G of groups. We show that with suitable algorithmic conditions on the free factors of G, one can effectively determine whether or not the equations have solutions in G. We also show that under certain hypotheses on the free factors of G and the equation itself, the equation W(x,y) = U has only finitely many solutions, up to the action of the stabilizer of W(x,y) in Aut().
C^1 Actions Of The Mapping Class Group On The Circle, Kamlesh Parwani
C^1 Actions Of The Mapping Class Group On The Circle, Kamlesh Parwani
Faculty Research and Creative Activity
Let S be a connected orientable surface with finitely many punctures, finitely many boundary components, and genus at least 6. Then any C^1 action of the mapping class group of S on the circle is trivial. The techniques used in the proof of this result permit us to show that products of Kazhdan groups and certain lattices cannot have C^1 faithful actions on the circle. We also prove that for n > 5, any C^1 action of Aut(F_n) or Out(F_n) on the circle factors through an action of Z/2Z.