Orbit Decidability, Applications and Variations

Ventura, Enric

doi:10.1007/978-3-319-05488-9_17

Trends in Mathematics

2014

DOI: 10.1007/978-3-319-05488-9_17

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Orbit Decidability, Applications and Variations

Enric Ventura

Abstract: The author thanks the CRM hospitality during the research programme on Automorphisms of Free Groups. He also acknowledges partial support from the Spanish Government through grant number MTM2011-25955.

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2016

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The conjugacy problem in extensions of Thompson’s group F

2016

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Abstract. We solve the twisted conjugacy problem on Thompson's group F . We also exhibit orbit undecidable subgroups of Aut(F ), and give a proof that Aut(F ) and Aut + (F ) are orbit decidable provided a certain conjecture on Thompson's group T is true. By using general criteria introduced by Bogopolski, Martino and Ventura in [5], we construct a family of free extensions of F where the conjugacy problem is unsolvable. As a byproduct of our techniques, we give a new proof of a result of showing that F has property R∞, and which can be extended to show that Thompson's group T also has property R∞.

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The conjugacy problem in extensions of Thompson’s group F

2016

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Orbit Decidability, Applications and Variations

Abstract: The author thanks the CRM hospitality during the research programme on Automorphisms of Free Groups. He also acknowledges partial support from the Spanish Government through grant number MTM2011-25955.

Cited by 1 publication

References 12 publications

The conjugacy problem in extensions of Thompson’s group F

The conjugacy problem in extensions of Thompson’s group F

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