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  • New techniques for computing geometric index
    Andrist, Kathryn B. ...
    We introduce new general techniques for computing the geometric index of a link ▫$L$▫ in the interior of a solid torus ▫$T$▫. These techniques simplify and unify previous ad hoc methods used to ... compute the geometric index in specific examples and allow a simple computation of geometric index for new examples where the index was not previously known. The geometric index measures the minimum number of times any meridional disc of ▫$T$▫ must intersect ▫$L$▫. It is related to the algebraic index in the sense that adding up signed intersections of an interior simple closed curve ▫$C$▫ in ▫$T$▫ with a meridional disc gives ▫$\pm$▫ the algebraic index of ▫$C$▫ in ▫$T$▫. One key idea is introducing the notion of geometric index for solid chambers of the form ▫$B^2 \times I$▫ in ▫$T$▫. We prove that if a solid torus can be divided into solid chambers by meridional discs in a specific (and often easy to obtain) way, then the geometric index can be easily computed.
    Source: Mediterranean journal of mathematics. - ISSN 1660-5446 (Vol. 14, iss. 6, 2017, art. 237 (15 str.))
    Type of material - article, component part ; adult, serious
    Publish date - 2017
    Language - english
    COBISS.SI-ID - 18167129

    Link(s):

    http://dx.doi.org/10.1007/s00009-017-1036-1
    Repository of the University of Ljubljana – RUL
    DOI

source: Mediterranean journal of mathematics. - ISSN 1660-5446 (Vol. 14, iss. 6, 2017, art. 237 (15 str.))
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