Symplectic knot spaces are the spaces of symplectic subspaces in a symplectic manifold M . We introduce a symplectic structure and show that the structure can be also obtained by the symplectic quotient method. We explain the correspondence between coisotropic submanifolds in M and Lagrangians in the symplectic knot space. We also define an almost complex structure on the symplectic knot space,...

The unknotting number of a knot is bounded from below by its slice genus. It is a well-known fact that the genera and unknotting numbers of torus knots coincide. In this note we characterize quasipositive knots for which the genus bound is sharp: the slice genus of a quasipositive knot equals its unknotting number, if and only if the given knot appears in an unknotting sequence of a torus knot.

We exhibit a knot P in the solid torus, representing a generator of first homology, such that for any knot K in the 3-sphere, the satellite knot with pattern P and companion K is not smoothly slice in any homology 4-ball. As a consequence, we obtain a knot in a homology 3-sphere that does not bound a piecewise-linear disk in any homology 4-ball. 2010 Mathematics Subject Classification: 57M27, 5...

It is known that knot Floer homology detects the genus and Alexander polynomial of a knot. We investigate whether knot Floer homology of K detects more structure of minimal genus Seifert surfaces for K. We define an invariant of algebraically slice, genus one knots and provide examples to show that knot Floer homology does not detect this invariant. Finally, we remark that certain metabelian L2...

We consider combinatorial maps with fixed combinatorial knot numbered with augmenting numeration called normalized knot. We show that knot’s normalization doesn’t affect combinatorial map what concerns its generality. Knot’s normalization leads to more concise numeration of corners in maps, e.g., odd or even corners allow easy to follow distinguished cycles in map caused by the fixation of the ...

The bridge index and superbridge index of a knot are important invariants in knot theory. We define the bridge map of a knot conformation, which is closely related to these two invariants, and interpret it in terms of the tangent indicatrix of the knot conformation. Using the concepts of dual and derivative curves of spherical curves as introduced by Arnold, we show that the graph of the bridge...

By a recent result of Livingston, it is known that if a knot has a prime power branched cyclic cover that is not a homology sphere, then there is an infinite family of nonconcordant knots having the same Seifert form as the knot. In this paper, we extend this result to the full extent. We show that if the knot has nontrivial Alexander polynomial, then there exists an infinite family of non-conc...

PURPOSE To assess the effect of cyanoacrylate glue on knot slippage and strength in vitro. METHODS Ethibond 3/0 was tested using a tensile tester. A single drop of cyanoacrylate glue was applied to the knots. Seven knot configurations (10 samples each) were tested: (1) a surgeon's knot (S) plus 4 square throws (+4) without glue (control group), (2) S plus one square throw (+1) without glue, (...

The cystine knot three-dimensional structure is found in many extracellular molecules and is conserved among divergent species. The identification of proteins with a cystine knot structure is difficult by commonly used pairwise alignments because the sequence homology among these proteins is low. Taking advantage of complete genome sequences in diverse organisms, we used a complementary approac...