TY - JOUR
T1 - The heegaard distances cover all nonnegative integers
AU - Qiu, Ruifeng
AU - Zou, Yanqing
AU - Guo, Qilong
PY - 2015
Y1 - 2015
N2 - We prove two main results: (1) For any integers n ≥ 1 and g ≥ 2, there is a closed 3-manifold Mng admitting a distance-n, genus-g Heegaard splitting, unless (g, n) = (2, 1). Furthermore, Mng can be chosen to be hyperbolic unless (g, n) = (3, 1). (2) For any integers g ≥ 2 and n ≥ 4, there are infinitely many nonhomeomorphic closed 3-manifolds admitting distance-n, genus-g Heegaard splittings.
AB - We prove two main results: (1) For any integers n ≥ 1 and g ≥ 2, there is a closed 3-manifold Mng admitting a distance-n, genus-g Heegaard splitting, unless (g, n) = (2, 1). Furthermore, Mng can be chosen to be hyperbolic unless (g, n) = (3, 1). (2) For any integers g ≥ 2 and n ≥ 4, there are infinitely many nonhomeomorphic closed 3-manifolds admitting distance-n, genus-g Heegaard splittings.
KW - Attaching handlebody
KW - Heegaard distance
KW - Subsurface projection
UR - https://www.scopus.com/pages/publications/84929230878
U2 - 10.2140/pjm.2015.275.231
DO - 10.2140/pjm.2015.275.231
M3 - 文章
AN - SCOPUS:84929230878
SN - 0030-8730
VL - 275
SP - 231
EP - 255
JO - Pacific Journal of Mathematics
JF - Pacific Journal of Mathematics
IS - 1
ER -