Abstract
AbstractWe prove that the mapping class group of the one‐holed Cantor tree surface is acyclic. This in turn determines the homology of the mapping class group of the once‐punctured Cantor tree surface (i.e. the plane minus a Cantor set), in particular answering a recent question of Calegari and Chen. We in fact prove these results for a general class of infinite‐type surfaces called binary tree surfaces. To prove our results we use two main ingredients: one is a modification of an argument of Mather related to the notion of dissipated groups; the other is a general homological stability result for mapping class groups of infinite‐type surfaces.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
