TY  - JOUR
AU  - Jaco, W
AU  - Rubinstein, JH
AU  - Sedgwick, E
Y2  - 2014/05/21
Y1  - 2009/03/01
SN  - 0218-2165
UR  - http://hdl.handle.net/11343/29232
AB  - It is shown that given any link-manifold, there is an algorithm to decide if the manifold contains an embedded, essential planar surface; if it does, the algorithm will construct one. Two similar results are obtained with added boundary conditions. Namely, given a link-manifold M, a component B of ∂M, and a slope γ on B, there is an algorithm to decide if there is an embedded punctured-disk in M with boundary γ and punctures in ∂M\B; and given a link-manifold M, a component B of ∂M, and a meridian slope μ on B, there is an algorithm to decide if there is an embedded punctured-disk with boundary a longitude on B and punctures in ∂M\B. In both cases, if there is one, the algorithm will construct one. The proofs introduce a number of new methods and differ from the classical proofs, using normal surfaces, as solutions may not be found among the fundamental solutions.
LA  - English
PB  - WORLD SCIENTIFIC PUBL CO PTE LTD
KW  - Pure Mathematics
T1  - FINDING PLANAR SURFACES IN KNOT- AND LINK-MANIFOLDS
DO  - 10.1142/S0218216509006987
IS  - Journal of Knot Theory and Its Ramifications
VL  - 18
IS  - 3
SP  - 397-446
L1  - /bitstream/handle/11343/29232/277940_135349.pdf?sequence=1&isAllowed=n
ER  -