相关论文: Bridged Links and Tangle Presentations of Cobordis…

We recall an extension of Kirby's Calculus on non-simply connected 3-manifolds given in [FR], and the surgery calculus of bridged links from [Ke], which involves only local moves. We give a short combinatorial proof that the two calculi are…

A celebrated theorem of Kirby identifies the set of closed oriented connected 3-manifolds with the set of framed links in $S^3$ modulo two moves. We give a similar description for the set of knots (and more generally, boundary links) in…

We show that only finitely many links in a closed 3-manifold share the same complement, up to twists along discs and annuli. Using the same techniques, we prove that by adding 2-handles on the same link we get only finitely many smooth…

In this paper we construct invariants of 3-manifolds "\`a la Reshetikhin-Turaev" in the setting of non-semi-simple ribbon tensor categories. We give concrete examples of such categories which lead to a family of 3-manifold invariants…

V.V. Sharko in his papers and books has investigated functions on manifolds and cobordism. Braids intimately connect with functions on manifolds. These connections are represented by mapping class groups of corresponding discs, by…

Tied links in $S^3$ were introduced by Aicardi and Juyumaya as standard links in $S^3$ equipped with some non-embedded arcs, called {\it ties}, joining some components of the link. Tied links in the Solid Torus were then naturally…

We show that simple coverings of B^4 branched over ribbon surfaces up to certain local ribbon moves bijectively represent orientable 4-dimensional 2-handlebodies up to handle sliding and addition/deletion of cancelling handles. As a…

This paper is the second part of our work on 4-dimensional 2-handlebodies. In the first part (arXiv:math.GT/0407032) it is shown that up to certain set of local moves, connected simple coverings of B^4 branched over ribbon surfaces,…

Let $B_n$ denote the classical braid group on $n$ strands and let the {\em mixed braid group} $B_{m,n}$ be the subgroup of $B_{m+n}$ comprising braids for which the first $m$ strands form the identity braid. Let…

Round handles are affiliated with smooth 4-manifolds in two major ways: 5-dimensional round handles appear extensively as the building blocks in cobordisms between 4-manifolds, whereas 4-dimensional round handles are the building blocks of…

This paper is concerned with detecting when a closed braid and its axis are 'mutually braided' in the sense of Rudolph. It deals with closed braids which are fibred links, the simplest case being closed braids which present the unknot. The…

We construct a cobordism group for embedded graphs in two different ways, first by using sequences of two basic operations, called "fusion" and "fission", which in terms of cobordisms correspond to the basic cobordisms obtained by attaching…

We study the effect of Nielsen moves and their geometric counterparts, handle slides, on good boundary links. A collection of links, universal for 4-dimensional surgery, is shown to admit Seifert surfaces with trivial Lagrangian. They are…

A special class of braids, called woven, is introduced and it is shown that every conjugation class of the braid group contains woven braids. In consequence, links can be presented as plats or closures of woven braids. Restricting on knots,…

We study the cobordism of manifolds with boundary, and its applications to codimension 2 embeddings $M^m\subset N^{m+2}$, using the method of the algebraic theory of surgery. The first main result is a splitting theorem for cobordisms of…

We show that two hypersurfaces in a manifold are related by a sequence of embedded cobordisms if and only if they represent the same homology class. By applying handle decompositions we turn these cobordisms into a sequence of embedded…

Bridge multisections are combinatorial descriptions of surface links in 4-space using tuples of trivial tangles. They were introduced by Islambouli, Karimi, Lambert-Cole, and Meier to study curves in rational surfaces. In this paper, we…

In this paper, we develop a theory of bordered $\mathit{HF}^-$ using the link surgery formula of Manolescu and Ozsv\'{a}th. We interpret their link surgery complexes as type-$D$ modules over an associative algebra $\mathcal{K}$, which we…

We show that a transverse link in a contact structure supported by an open book decomposition can be transversely braided. We also generalize Markov's theorem on when the closures of two braids represent (transversely) isotopic links.

We extend Turaev's definition of torsion invariants of 3-dimensional manifolds equipped with non-singular vector fields, by allowing (suitable) tangency circles to the boundary, and manifolds with non-zero Euler characteristic. We show that…