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Necessary and Sufficrent Geometric Conditions
Jaeik Lee,Jongnyun Lee 한국산업응용수학회 2005 한국산업응용수학회 학술대회 논문집 Vol.- No.-
This Paper deals with a geometric criterion for checking the incompressibility of ∂Hk-Γ, where Hk, and Γdenotes an orientable handle body of genus k and a finite system of pairwise disjoint simple closed curves in ∂Hk. Our theorem will turn out to be very applicable for various surfaces in Hk, and give us a visual approach in detecting the incompressibility of ∂Hk-Γ. So it provides us with useful information about compressing disks for ∂Hk-Γ when ∂Hk-Γ is compressible in Hk.