Izvorni znanstveni članak

https://doi.org/10.3336/gm.55.1.07

Centers of subgroups of big mapping class groups and the Tits alternative

Justin Lanier orcid.org/0000-0003-4483-8553 ; School of Mathematics, Georgia Institute of Technology, 686 Cherry St., Atlanta, GA 30332, USA
Marissa Loving ; Department of Mathematics, University of Illinois, 1409 W. Green Street, Urbana, IL 61801, USA

Sažetak

In this note we show that many subgroups of mapping class groups of infinite-type surfaces without boundary have trivial centers, including all normal subgroups. Using similar techniques, we show that every nontrivial normal subgroup of a big mapping class group contains a nonabelian free group. In contrast, we show that no big mapping class group satisfies the strong Tits alternative enjoyed by finite-type mapping class groups. We also give examples of big mapping class groups that fail to satisfy even the classical Tits alternative; consequently, these examples are not linear.

Ključne riječi

Mapping class groups; normal subgroups; free subgroups; Tits alternative; centers

Hrčak ID:

239048

URI

https://hrcak.srce.hr/239048

Datum izdavanja:

12.6.2020.

Posjeta: 1.160 *