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21#
發(fā)表于 2025-3-25 06:23:09 | 只看該作者
Guts and Fibers,This chapter contains one of the main results of the manuscript, namely a calculation of the Euler characteristic of the guts of .. in Theorem 5.14. The calculation will be in terms of the number of essential product disks (EPDs) for .. which are ., as in Definition 5.2, below.
22#
發(fā)表于 2025-3-25 08:04:00 | 只看該作者
Montesinos Links,In this chapter, we study state surfaces of Montesinos links, and calculate their guts. Our main result is Theorem 8.6. In that theorem, we show that for every sufficiently complicated Montesinos link ., either . or its mirror image admits an .-adequate diagram . such that the quantity . of Definition 5.9 vanishes.
23#
發(fā)表于 2025-3-25 13:21:07 | 只看該作者
24#
發(fā)表于 2025-3-25 17:00:38 | 只看該作者
25#
發(fā)表于 2025-3-25 22:51:57 | 只看該作者
https://doi.org/10.1007/978-3-031-40098-8omposition includes no non-prime arcs or switches. In this case, one can simplify the statement of Theorem 5.14 and give an easier combinatorial estimate for the guts of ... This is done in Theorem 7.2, whose proof takes up the bulk of the chapter.
26#
發(fā)表于 2025-3-26 00:13:33 | 只看該作者
27#
發(fā)表于 2025-3-26 07:11:36 | 只看該作者
Introduction,r areas of mathematics and from physics. On the one hand, ideas from geometry have led to geometric decompositions of 3-manifolds and to invariants such as the .-polynomial and hyperbolic volume. On the other hand, ideas from quantum physics have led to the development of invariants such as the Jones polynomial and colored Jones polynomials.
28#
發(fā)表于 2025-3-26 08:31:20 | 只看該作者
Recognizing Essential Product Disks,bundle of the upper polyhedron. Our purpose in this chapter is to recognize such EPDs from the structure of the all-. state graph .. The main result is Theorem 6.4, which describes the basic building blocks for such EPDs.
29#
發(fā)表于 2025-3-26 16:43:33 | 只看該作者
Diagrams Without Non-prime Arcs,omposition includes no non-prime arcs or switches. In this case, one can simplify the statement of Theorem 5.14 and give an easier combinatorial estimate for the guts of ... This is done in Theorem 7.2, whose proof takes up the bulk of the chapter.
30#
發(fā)表于 2025-3-26 17:08:34 | 只看該作者
Discussion and Questions, we discuss modifications of the diagram . that preserve .-adequacy. In Sect. 10.2, we speculate about using normal surface theory in our polyhedral decomposition of .. to attack various open problems, for example the Cabling Conjecture and the determination of hyperbolic .-adequate knots.
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