منابع مشابه
Algebraic Functions and Closed Braids
LET f (z,w) ≡ f0(z)w + f1(z)w + · · · + fn(z) ∈ C[z,w]. Classically, the equation f (z,w) = 0 was said to define w as an (n-valued) algebraic function of z, provided that f0(z) was not identically 0 and that f (z,w) was squarefree and without factors of the form z− c. Then, indeed, the singular set B = {z: there are not n distinct solutions w to f (z,w) = 0} is finite; and as z varies in any si...
متن کاملClosed Braids and Heegaard Splittings
In this note we will be investigating a strategy for constructing 3-manifolds that have multiple strongly irreducible Heegaard splittings that are not equivalent. This strategy combines techiques involving framed links and a calculus on closed braids developed by Joan Birman and the author.
متن کاملIsotopy invariants for closed braids and almost closed braids via loops in stratified spaces
Let φ : S ×D → S be the natural projection. An oriented knot K →֒ V = S ×D is called an almost closed braid if the restriction of φ to K has exactly two (non-degenerate) critical points (and K is a closed braid if the restriction of φ has no critical points at all). We introduce new isotopy invariants for closed braids and almost closed braids in the solid torus V. These invariants refine finite...
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A braided n-path is a set of « paths ct(t) in R 3 (i = 1 , . . . , n) satisfying (1) c,(0 = (*,(>), MO, 0> ' i < * < r2, c ^ ) = P„ C/(r2) e { & , . . ,Ô„}(2) The paths do not intersect. Two braided «-paths are regarded as equivalent if and only if it is possible to deform the one configuration into the other respecting conditions (1) and (2) throughout the deformation; note that one does permi...
متن کاملOn the Kinkiness of Closed Braids
In this note, we prove a lower bound for the positive kinkiness of a closed braid which we then use to derive an estimate for the positive kinkiness of a link in terms of its Seifert system. As an application, we show that certain pretzel knots cannot be unknotted using only positive crossing changes. We also describe a subgroup of infinite rank in the smooth knot concordance group of which no ...
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ژورنال
عنوان ژورنال: Topology
سال: 1983
ISSN: 0040-9383
DOI: 10.1016/0040-9383(83)90031-9