共查询到20条相似文献,搜索用时 10 毫秒
1.
《Topology and its Applications》2005,146(2-3):303-317
We introduce new operations reducing the number of Seifert circles in link diagrams of a special type. The operations are similar to one described in [Mem. Amer. Math. Soc. 508 (1993)] and [Math. Proc. Cambridge Philos. Soc. 111 (2) (1992) 273]. We discuss a conjecture about the number of Seifert circles that can be canceled by applying the operation repeatedly. We translate the problem into one belonging to graph theory. 相似文献
2.
Morton and Franks–Williams independently gave a lower bound for the braid index b(L) of a link L in S3 in terms of the v-span of the Homfly-pt polynomial PL(v,z) of L: . Up to now, many classes of knots and links satisfying the equality of this Morton–Franks–Williams's inequality have been founded. In this paper, we give a new such a class of knots and links and make an explicit formula for determining the braid index of knots and links that belong to the class . This gives simultaneously a new class of knots and links satisfying the Jones conjecture which says that the algebraic crossing number in a minimal braid representation is a link invariant. We also give an algorithm to find a minimal braid representative for a given knot or link in . 相似文献
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David Cimasoni Vincent Florens 《Transactions of the American Mathematical Society》2008,360(3):1223-1264
In this paper, we use `generalized Seifert surfaces' to extend the Levine-Tristram signature to colored links in . This yields an integral valued function on the -dimensional torus, where is the number of colors of the link. The case corresponds to the Levine-Tristram signature. We show that many remarkable properties of the latter invariant extend to this -variable generalization: it vanishes for achiral colored links, it is `piecewise continuous', and the places of the jumps are determined by the Alexander invariants of the colored link. Using a -dimensional interpretation and the Atiyah-Singer -signature theorem, we also prove that this signature is invariant by colored concordance, and that it provides a lower bound for the `slice genus' of the colored link.
5.
Michael Hutchings 《Transactions of the American Mathematical Society》1998,350(5):1791-1809
We prove necessary and sufficient conditions for an arbitrary invariant of braids with double points to be the `` derivative' of a braid invariant. We show that the ``primary obstruction to integration' is the only obstruction. This gives a slight generalization of the existence theorem for Vassiliev invariants of braids. We give a direct proof by induction on which works for invariants with values in any abelian group.
We find that to prove our theorem, we must show that every relation among four-term relations satisfies a certain geometric condition. To find the relations among relations we show that of a variant of Kontsevich's graph complex vanishes. We discuss related open questions for invariants of links and other things.
6.
Jeró nimo Dí az-Cantos Juan Gonzá lez-Meneses José M. Tornero 《Proceedings of the American Mathematical Society》2004,132(10):2867-2873
In this paper we show that the singular braid monoid of an orientable surface can be embedded in a group. The proof is purely topological, making no use of the monoid presentation.
7.
L. P. Plachta 《Journal of Mathematical Sciences》2010,170(5):567-579
We study the relationship between reduction operations on link diagrams and S-graphs associated with them. We are motivated by the problem of computing the braid index of a link and some well known conjectures concerning the braid index of a link and the writhe of its diagrams. Possible counterexamples are discussed in terms of both S-graphs and link diagrams. We also indicate the relation of S-graphs to singular links regarded up to an appropriate equivalence relation. 相似文献
8.
Jessica E. Banks 《Geometriae Dedicata》2013,166(1):67-98
We give a geometric proof of the following result of Juhasz. Let a g be the leading coefficient of the Alexander polynomial of an alternating knot K. If |a g | < 4 then K has a unique minimal genus Seifert surface. In doing so, we are able to generalise the result, replacing ‘minimal genus’ with ‘incompressible’ and ‘alternating’ with ‘homogeneous’. We also examine the implications of our proof for alternating links in general. 相似文献
9.
Virtual singular braids are generalizations of singular braids and virtual braids. We define the virtual singular braid monoid via generators and relations, and prove Alexander- and Markov-type theorems for virtual singular links. We also show that the virtual singular braid monoid has another presentation with fewer generators. 相似文献
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Tsuyoshi Kobayashi 《Topology and its Applications》1985,20(1):67-78
In this paper we consider a non-singular Morse-Smale flow Φt on an irreducible, simple, closed, orientable 3-manifold M. We define a primitive flow ψt from Φt, and call the link type of the closed orbits of ψt a primitive link of Φt. We show that the link types of the primitive links are finite and every non-singular Morse-Smale flow on M is obtained from a primitive flow by exchanging the flow in a regular neighborhood of attracting or repelling closed orbits. 相似文献
12.
Irene Sciriha 《Journal of Mathematical Sciences》2012,182(2):117-125
A graph G is singular if the nullspace of its adjacency matrix is nontrivial. Such a graph contains induced subgraphs called singular configurations of nullity 1. We present two algorithms. One is for the construction of a maximal singular nontrivial graph G containing an induced subgraph, which is a singular configuration with the support of a vector in its nullspace as in that of G. The second is for the construction of a nut graph, a graph of nullity one whose null vector has no zero entries. An extremal singular graph of a given order, with the maximal nullity and support, has a nut graph as a maximal singular configuration. 相似文献
13.
《Topology and its Applications》2004,135(1-3):13-31
The Morton–Franks–Williams inequality for a link gives a lower bound for the braid index in terms of the HOMFLY polynomial. Franks and Williams conjectured that for any closed positive braid the lower bound coincides with the braid index. In this paper, we show that the bound is achieved for a certain class of closed positive braids. We also give an infinite family of prime closed positive braids such that the lower bound does not coincide with their braid indices. 相似文献
14.
The main purpose of this paper is to show that any embedding of K7 in three-dimensional euclidean space contains a knotted cycle. By a similar but simpler argument, it is also shown that any embedding of K6 contains a pair of disjoint cycles which are homologically linked. 相似文献
15.
Furihata Rei; Hirasawa Mikami; Kobayashi Tsuyoshi 《Bulletin London Mathematical Society》2008,40(3):405-414
We show that for any link L, there exists a Seifert surfacefor L that is obtained by successively plumbing flat annulito a disk D, where the gluing regions are all in D. This furnishesa new way of coding links. We also present an algorithm to readthe code directly from a braid presentation. 相似文献
16.
Milan Nath 《Linear algebra and its applications》2007,427(1):42-54
For acyclic and unicyclic graphs we determine a necessary and sufficient condition for a graph G to be singular. Further, it is shown that this characterization can be used to construct a basis for the null-space of G. 相似文献
17.
This paper finishes the classification of the finite primitive affine distance-transitive graphs by dealing with the only case left open, namely where the generalized Fitting subgroup of the stabilizer of a vertex is modulo scalars a simple group of classical Lie type defined over the characteristic dividing the number of vertices of the graph. All graphs that are found to occur are known. 相似文献
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Chichen M. Tsau 《Proceedings of the American Mathematical Society》2001,129(8):2497-2502
We show that two isotopic oriented 4-valent singular link diagrams with transverse intersections are regularly isotopic if and only if they have the same writhe and the same rotation number.
20.
Ginette Gauyacq 《Discrete Applied Mathematics》1997,80(2-3):149-160
We present a technique for building, in some Cayley graphs, a routing for which the load of every edge is almost the same. This technique enables us to find the edge-forwarding index of star graphs and complete-transposition graphs. 相似文献