5 citations · 6 across the 8 of their papers we have counts for
9 papers
Mapping class groups have a unique Polish group structure
Tyrone Ghaswala, Sumun Iyer, Robert Alonzo Lyman +1
We prove that mapping class groups of surfaces and of locally finite connected graphs support a unique Polish group structure.
Universal minimal flows of homeomorphism groups of continua
Sumun Iyer
We define a combinatorial property of a projective Fraisse category which we call the \emph{approximate Ramsey property}. Let be a continuum, a closed subgroup of the homeo…
Asymptotic dimension and hyperfiniteness of generic Cantor actions
Sumun Iyer, Forte Shinko
We show that for a countable discrete group which is locally of finite asymptotic dimension, the generic continuous action on Cantor space has hyperfinite orbit equivalence relatio…
A Ramsey-type phenomenon in two and three dimensional simplices
Sumun Iyer
We develop a Ramsey-like theorem for subsets of the two and three-dimensional simplex. A generalization of the combinatorial theorem presented here to all dimensions would produce…
Direct limits of large orbits and the Knaster continuum homeomorphism group
Sumun Iyer
The main result is that the group of homeomorphisms of the universal Knaster continuum contains an open subgroup with a comeager conjugacy class. Actually, thi…
The homeomorphism group of the universal Knaster continuum
Sumun Iyer
We define a projective Fraissé family whose limit approximates the universal Knaster continuum. The family is such that the group of automorphisms of the…
Tiling Billards on Triangle Tilings, and Interval Exchange Transformations
Paul Baird-Smith, Diana Davis, Elijah Fromm +1
We consider the dynamics of light rays in triangle tilings where triangles are transparent and adjacent triangles have equal but opposite indices of refraction. We find that the be…
Star coloring splitting graphs of cycles
Sumun Iyer
A star coloring of a graph is a proper vertex coloring such that the subgraph induced by any pair of color classes is a star forest. The star chromatic number of is the min…
Domination and Upper Domination of Direct Product Graphs
Colin Defant, Sumun Iyer
The unitary Cayley graph of , denoted , has vertices with adjacent to if is relatively prim…