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LINES JOINING COMPONENTS OF A LINK

JULIA VIRO

Department of Mathematics, Stony Brook University, Stony Brook NY, 11794-3651, USA

https://doi.org/10.1142/S0218216509007221Cited by:2 (Source: Crossref)

Abstract

We estimate from below the number of lines meeting each of given 4 disjoint smooth closed curves in a given cyclic order in the real projective 3-space. We obtain also a similar lower bound for the number of lines meeting each of given 4 disjoint smooth closed curves in a given linear order in ℝ³. The estimates are formulated in terms of linking numbers of the curves and obtained by orienting of the corresponding configuration spaces and evaluating of their signatures. This involves a study of a surface swept by lines meeting 3 given disjoint smooth closed curves. Higher-dimensional generalizations of these results are outlined.

Keywords:

AMSC: 57M25, 57Q45

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