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We deal with Matveev complexity of compact orientable 3-manifolds represented via Heegaard diagrams.
This lead us to the definition of modified Heegaard complexity of Heegaard diagrams and of manifolds. We define a class of manifolds which are generalizations of Dunwoody manifolds, including cyclic branched coverings of two-bridge knots and links, torus knots, some pretzel knots, and some theta-graphs.
Using modified Heegaard complexity, we obtain upper bounds for their Matveev complexity, which linearly depend on the order of the covering. Moreover, using homology arguments due to Matveev and Pervova we obtain lower bounds.
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참고문헌 (26)
참고문헌 신청
A. Cattabriga / 2004 / All strongly-cyclic branched coverings of (1, 1)-knots are Dunwoody manifolds / J. London Math. Soc. 70 (2) : 512 ~ 528
A. Cattabriga / 2005 / Representations of (1, 1)-knots / Fund. Math. 188 : 45 ~ 57
A. Cavicchioli / 1988 / On some properties of the groups G(n, l) / Ann. Mat. Pura Appl. 151 (4) : 303 ~ 316
A. Kawauchi / 1996 / A Survey of Knot Theory / Birkh¨auser
C. Petronio / / Two-sided bounds for the complexity of cyclic branched coverings of two-bridge links, preprint, arXiv:math.GT/0612830v2
A. Cattabriga / 2005 / Representations of (1, 1)-knots / Fund. Math. 188 : 45 ~ 57
A. Cavicchioli / 1988 / On some properties of the groups G(n, l) / Ann. Mat. Pura Appl. 151 (4) : 303 ~ 316
A. Kawauchi / 1996 / A Survey of Knot Theory / Birkh¨auser
C. Petronio / / Two-sided bounds for the complexity of cyclic branched coverings of two-bridge links, preprint, arXiv:math.GT/0612830v2
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