NOTIONS OF POSITIVITY AND THE OZSVATH-SZABO CONCORDANCE INVARIANT

作者：Hedden Matthew^*

来源：Journal of Knot Theory and Its Ramifications, 2010, 19(5): 617-629.

DOI：10.1142/S0218216510008017

• Quasipositive
• braid
• knot
• concordance
• Floer homology
• contact geometry
• algebraic curve

In this paper we examine the relationship between various types of positivity for knots and the concordance invariant tau discovered by Ozsvath and Szabo and independently by Rasmussen. The main result shows that, for fibered knots, tau characterizes strong quasipositivity. This is quantified by the statement that for K fibered, tau(K) = g(K) if and only if K is strongly quasipositive. A corollary is that any knot admitting a lens space surgery or, more generally, an L-space surgery, is strongly quasipositive. In addition, we survey existing results regarding tau and forms of positivity and highlight several consequences concerning the types of knots which are (strongly) (quasi) positive.

• 出版日期2010-5