6 citations · 12 across the 6 of their papers we have counts for
6 papers
The complexity of prime 3-manifolds and the first -cohomology of small rank
Kei Nakamura
For a closed orientable connected 3-manifold , its complexity is defined to be the minimal number of tetrahedra in its triangulations. Under the assumption t…
Geometry and Arithmetic of Crystallographic Sphere Packings
Alex Kontorovich, Kei Nakamura
We introduce the notion of a "crystallographic sphere packing," defined to be one whose limit set is that of a geometrically finite hyperbolic reflection group in one higher dimens…
The local-global principle for integral bends in orthoplicial Apollonian sphere packings
Kei Nakamura
We introduce an orthoplicial Apollonian sphere packing, which is a sphere packing obtained by successively inverting a configuration of 8 spheres with 4-orthplicial tangency graph.…
On Isosystolic Inequalities for T^n, RP^n, and M^3
Kei Nakamura
If a closed smooth n-manifold M admits a finite cover whose Z/2Z-cohomology has the maximal cup-length, then for any riemannian metric g on M, we show that the systole Sys(M,g) and…
Fox reimbedding and Bing submanifolds
Kei Nakamura
Let M be an orientable closed connected 3-manifold. We introduce the notion of amalgamated Heegaard genus of M with respect to a closed separating 2-manifold F, and use it to show…
The girth alternative for mapping class groups
Kei Nakamura
The girth of a finitely generated group G is the supremum of the girth of Cayley graphs for G over all finite generating sets. Let G be a finitely generated subgroup of the mapping…