92 research outputs found
Asymmetric hyperbolic L-spaces, Heegaard genus, and Dehn filling
An L-space is a rational homology 3-sphere with minimal Heegaard Floer
homology. We give the first examples of hyperbolic L-spaces with no symmetries.
In particular, unlike all previously known L-spaces, these manifolds are not
double branched covers of links in S^3. We prove the existence of infinitely
many such examples (in several distinct families) using a mix of hyperbolic
geometry, Floer theory, and verified computer calculations. Of independent
interest is our technique for using interval arithmetic to certify symmetry
groups and non-existence of isometries of cusped hyperbolic 3-manifolds. In the
process, we give examples of 1-cusped hyperbolic 3-manifolds of Heegaard genus
3 with two distinct lens space fillings. These are the first examples where
multiple Dehn fillings drop the Heegaard genus by more than one, which answers
a question of Gordon.Comment: 19 pages, 2 figures. v2: minor changes to intro. v3: accepted
version, to appear in Math. Res. Letter
A duplicate pair in the SnapPea census
We identify a duplicate pair in the well-known Callahan-Hildebrand-Weeks
census of cusped finite-volume hyperbolic 3-manifolds. Specifically, the
six-tetrahedron non-orientable manifolds x101 and x103 are homeomorphic.Comment: 5 pages, 3 figures; v2: minor edits. To appear in Experimental
Mathematic
Euclidean decompositions of hyperbolic manifolds and their duals
Epstein and Penner constructed in [EP88] the Euclidean decomposition of a non-compact hyperbolic n-manifold of finite volume for a choice of cusps, n >= 2. The manifold is cut along geodesic hyperplanes into hyperbolic ideal convex polyhedra. The intersection of the cusps with the Euclidean decomposition determined by them turns out to be rather simple as stated in Theorem 2.2. A dual decomposition resulting from the expansion of the cusps was already mentioned in [EP88]. These two dual hyperbolic decompositions of the manifold induce two dual decompositions in the Euclidean structure of the cusp sections. This observation leads in Theorems 5.1 and 5.2 to easily computable, necessary conditions for an arbitrary ideal polyhedral decomposition of the manifold to be a Euclidean decomposition
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