11
$\begingroup$

In the paper A faithful linear-categorical action of the mapping class group of a surface with boundary it is claimed that it was (as of 2014) still unknown that mapping class group is linear, but the authors provide a faithful linear-categorical action of the mapping class group of a surface with necessarily non-empty boundary using knot Floer homology that does not seem decategorifiable in a non-trivial way.

On the other hand, there exists the following paper, Mapping class groups are linear, in which the author uses the non-commutative machinery to prove that they are. As I have asked in this question, there might perhaps be a mistake in one of the proof ingredients.

Hence the question: is it known that a mapping class group of some surface (possibly with non-empty boundary or non-zero number of punctures) is linear?

Improve this question
$\endgroup$
2
  • 1
    $\begingroup$ I changed the arXiv links to point to the abstract pages. $\endgroup$
    – David Roberts ♦
    Sep 2, 2015 at 6:43
  • 2
    $\begingroup$ The paper ``Mapping class groups are linear'' was published in 2018 as part of the de Gruyter book Topological Algebras and Their Applications: Proceedings of the 8th International Conference on Topological Algebras and Their Applications, 2014. Is the paper believed to be correct at this point, or is this still under dispute? $\endgroup$
    – Jim Belk
    Nov 14, 2021 at 0:02

1 Answer 1

Reset to default
6
$\begingroup$

Yes. There is the paper by Bigelow, and our own Ryan Budney, who do this for genus 2. I believe that is still the last word.

Improve this answer
$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge that you have read and understand our privacy policy and code of conduct.

Not the answer you're looking for? Browse other questions tagged or ask your own question.