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      Universal Vassiliev invariants of links in coverings of 3-manifolds

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          Abstract

          We study Vassiliev invariants of links in a 3-manifold M by using chord diagrams labeled by elements of the fundamental group of M. We construct universal Vassiliev invariants of links in M, where M=P2×[0,1] is a cylinder over the real projective plane P2, M=Σ×[0,1] is a cylinder over a surface Σ with boundary, and M=S1×S2. A finite covering p:NM induces a map π1(p) between labeled chord diagrams that corresponds to taking the preimage p1(L)N of a link LM. The maps p1 and π1(p) intertwine the constructed universal Vassiliev invariants.

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          Author and article information

          Journal
          02 May 2001
          Article
          math/0105019
          403ca9e1-1f1e-4bce-94bb-e361288be71c
          History
          Custom metadata
          57M25
          46 pages, many figures
          math.QA

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