ALGEBRAIC FUNCTIONS AND CLOSED BRAIDS

By Lee Rudolph. 2004

144 citations recorded by the source corpus.

This article was originally published in Topology 22 (1983). The present hyperTeXed redaction includes references to post-1983 results as Addenda, and corrects a few typographical errors. (See math.GT/0411115 for a more comprehensive overview of the subject as it appears 21 years later.)

Subfields: Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/e5de9d0d8dcb60945ad4ce587425d0e69c7057fa

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Citations in the corpus

NOTIONS OF POSITIVITY AND THE OZSVÁTH–SZABÓ CONCORDANCE INVARIANT (2005, background): “1 <=> 2 We use Giroux’s fundamental theorem in contact geometry together with a theorem of Rudolph.”
Fibered Transverse Knots and the Bennequin Bound (2008, methodology): “ By way of motivation for this deﬁnition we note that quasi-positive links are precisely those that are formed by transversely intersecting the unit 3-sphere in C2 with a complex analytic plane curve [2, 27]. Moreover Orevkov has an approach to Hilbert’s sixteenth problem concerning real algebraic c”
Knot Theory of Complex Plane Curves (2004, background): “s is solidly part of modern knot theory—the knots and links in question are C-links, and the extra structures variously algebraic, analytic, and geometric. “Some knot theory of complex plane curves” (Rudolph, 1983d) was a broad view of the state of the art in 1982. Here I propose to look at the subj”
On braid monodromy factorizations (2003, background): “e we give an almost pure algebraic proof of a recent result due to S. Orevkov [19], which states that any bmf over a disc can be realized by an algebraic curve (and which generalizes Rudolf’s theorem [20] on algebraic realization of quasi-positive braids). In our construction the curve seats in a ru”
Compact Stein surfaces with boundary as branched covers of B4 (2000, background): “Its proof is implicit in [34] (see remark 4.”
On knot Floer homology and cabling (2004, background): “≥ 0. Then n ≥ −2 τ(K) p−1 + 1 p . ON KNOT FLOER HOMOLOGY AND CABLING II 19 This is relevant in light of the connection between τ(K) and complex curves. Suppose that K is a C-knot. Then results of [31, 13, 36] show that τ(K) = g 4(K). In particular, τ(K) ≥ 0. Combining this fact with the corollary ”
On Knot Floer Homology and Cabling: 2 (2008, background): “Results of [36] and [3] indicate that C-knots are exactly the class of knots obtained as the closures of quasipositive braids.”