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ON A BASIS FOR THE FRAMED LINK VECTOR SPACE SPANNED BY CHORD DIAGRAMS

BRYAN BISCHOF

Department of Mathematics, Kansas State University, Manhattan, KS 66506, USA

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ROMAN KOGAN

SUNY Stony Brook, Stony Brook, NY 11794, USA

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, and

DAVID N. YETTER

Department of Mathematics, Kansas State University, Manhattan, KS 66506, USA

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https://doi.org/10.1142/S0218216509007683Cited by:0 (Source: Crossref)

Abstract

In view of the result of Kontsevich, now often called "the fundamental theorem of Vassiliev theory", identifying the graded dual of the associated graded vector space to the space of Vassiliev invariants filtered by degree with the linear span of chord diagrams modulo the "4T-relation" (and in the unframed case, originally considered by Vassiliev, the "1T-" or "isolated chord relation"), it is a problem of some interest to provide a basis for the space of chord diagrams modulo the 4T-relation.

We construct the basis for the vector space spanned by chord diagrams with n chords and m link components, modulo 4T relations for n ≤ 5.

Keywords:

AMSC: 57M27

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