6 citations · 12 across the 11 of their papers we have counts for
12 papers
Homeomorphism groups of 2-manifolds with the virtual Rokhlin property
Justin Lanier, Nicholas G. Vlamis
We introduce and motivate the definition of the virtual Rokhlin property for topological groups. We then classify the 2-manifolds whose homeomorphism groups have the virtual Rokhli…
The normal closure of a bounding pair map in its mapping class group
Lei Chen, Weiyan Chen, Justin Lanier
Johnson showed that the normal subgroup of a mapping class group generated by the genus bounding pair maps is equal to the Torelli group. Generalizing Johnson's result, we give…
Twisting cubic rabbits
Justin Lanier, Rebecca R. Winarski
We solve an infinite family of twisted polynomial problems that are cubic generalizations of Hubbard's twisted rabbit problem. We show how the result of twisting by a power of a ce…
Constraining mapping class group homomorphisms using finite subgroups
Lei Chen, Justin Lanier
We classify homomorphisms from mapping class groups by using finite subgroups. First, we give a new proof of a result of Aramayona--Souto that homomorphisms between mapping class g…
Curve graphs of surfaces with finite-invariance index 1
Justin Lanier, Marissa Loving
In this note we make progress toward a conjecture of Durham--Fanoni--Vlamis, showing that every infinite-type surface with finite-invariance index 1 and no nondisplaceable compact…
Mapping class groups with the Rokhlin property
Justin Lanier, Nicholas G. Vlamis
We classify the connected orientable 2-manifolds whose mapping class groups have a dense conjugacy class. We also show that the mapping class group of a connected orientable 2-mani…
Recognizing topological polynomials by lifting trees
James Belk, Justin Lanier, Dan Margalit +1
We give a simple algorithm that determines whether a given post-critically finite topological polynomial is Thurston equivalent to a polynomial. If it is, the algorithm produces th…
Centers of subgroups of big mapping class groups and the Tits alternative
Justin Lanier, Marissa Loving
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 tech…
Adding a point to configurations in closed balls
Lei Chen, Nir Gadish, Justin Lanier
We answer the question of when a new point can be added in a continuous way to configurations of distinct points in a closed ball of arbitrary dimension. We show that this is p…
How to hear the shape of a billiard table
Aaron Calderon, Solly Coles, Diana Davis +2
The bounce spectrum of a polygonal billiard table is the collection of all bi-infinite sequences of edge labels corresponding to billiard trajectories on the table. We give methods…
Normal generators for mapping class groups are abundant
Justin Lanier, Dan Margalit
We provide a simple criterion for an element of the mapping class group of a closed surface to have normal closure equal to the whole mapping class group. We apply this to show tha…
Generating mapping class groups with elements of fixed finite order
Justin Lanier
We show that for any at least and sufficiently large, the mapping class group of a surface of genus can be generated by three elements of order . We also show th…