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학술연구/단체지원/교육 등 연구자 활동을 지속하도록 DBpia가 지원하고 있어요.
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초록· 키워드
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Let M=H_1∪s H_2 be a Heegaard splitting of a 3-manifold M, D be an essential disk in H_1 and A be an essential annulus in H_2. Suppose D and A intersect in one point.
First, we show that a Heegaard splitting admitting such a (D,A) pair satisfies the disjoint curve property, yet there are infinitely many examples of strongly irreducible Heegaard splittings with such (D,A) pairs.
In the second half, we obtain another Heegaard splitting M=H'_1∪{S'} H'_2 by removing the neighborhood of A from H_2 and attaching it to H_1, and show that M=H'_1∪{S'} H'_2 also has a (D,A) pair with │D∩A│=1.
목차
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참고문헌 (8)
참고문헌 신청
A. Casson / / Manifolds with irreducible Heegaard splittings of arbitrary large genus
A. Casson / 1987 / Reducing Heegaard splittings / Topology Appl. 27 (3) : 275 ~ 283
A. Thompson / 1999 / The disjoint curve property and genus 2 manifolds / Topology 97 (3) : 273 ~ 279
J. Hempel / 2001 / 3-manifolds as viewed from the curve complex / Topology 40 (3) : 631 ~ 657
J. Schultens / 2000 / Additivity of tunnel number for small knots / Comment. Math. Helv. 75 (3) : 353 ~ 367
A. Casson / 1987 / Reducing Heegaard splittings / Topology Appl. 27 (3) : 275 ~ 283
A. Thompson / 1999 / The disjoint curve property and genus 2 manifolds / Topology 97 (3) : 273 ~ 279
J. Hempel / 2001 / 3-manifolds as viewed from the curve complex / Topology 40 (3) : 631 ~ 657
J. Schultens / 2000 / Additivity of tunnel number for small knots / Comment. Math. Helv. 75 (3) : 353 ~ 367
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