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math.GT2026
The Torelli Group and Euler Class Zero Representations
Marit Bobb, James Farre, Peter Smillie
We prove that every representation of a closed surface group of genus at least into that is sufficiently close (but not equal to) a representation…
math.GT2023
Exact enumeration of fullerenes
Philip Engel, Jan Goedgebeur, Peter Smillie
A fullerene, or buckyball, is a trivalent graph on the sphere with only pentagonal and hexagonal faces. Building on ideas of Thurston, we use modular forms to give an exact formula…
math.GT2017★ 15 cited
The number of convex tilings of the sphere by triangles, squares, or hexagons
Philip Engel, Peter Smillie
A tiling of the sphere by triangles, squares, or hexagons is convex if every vertex has at most 6, 4, or 3 polygons adjacent to it, respectively. Assigning an appropriate weight to…