Local uniqueness of certain geodesics related to Heegaard splittings
2018 ◽
Vol 27
(09)
◽
pp. 1842003
Keyword(s):
Suppose [Formula: see text] is a Heegaard splitting and [Formula: see text] is an essential separating disk in [Formula: see text] such that a component of [Formula: see text] is homeomorphic to [Formula: see text], [Formula: see text]. In this paper, we prove that if there is a locally complicated simplicial path in [Formula: see text] connecting [Formula: see text] to [Formula: see text], then the geodesic connecting [Formula: see text] to [Formula: see text] is unique. Moreover, we give a sufficient condition such that [Formula: see text] is keen and the geodesic between any pair of essential disks on the opposite sides has local uniqueness property.
2018 ◽
Vol 27
(01)
◽
pp. 1850005
◽
Keyword(s):
2012 ◽
Vol 21
(08)
◽
pp. 1250078
Keyword(s):
2019 ◽
Vol 28
(09)
◽
pp. 1950059
2003 ◽
Vol 12
(05)
◽
pp. 579-588
2013 ◽
Vol 22
(05)
◽
pp. 1350018
◽
2010 ◽
Vol 149
(1)
◽
pp. 115-125
Keyword(s):
2013 ◽
Vol 22
(11)
◽
pp. 1350065
◽
2014 ◽
Vol 178
◽
pp. 345-351
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Keyword(s):