Linking numbers in non-orientable 3-manifolds

2016/06/19 by Victor A. Vassiliev, Vassiliev, Victor A.
Mathematics · #57M27 #FOS: Mathematics #Geometric Topology (math.GT) #math.GT #msc:57M27

paper · pdf · doi:10.48550/arxiv.1606.05876

arxiv created 2016/06/19 · arxiv updated 2016/06/21

Abstract

The construction of integer linking numbers of closed curves in a three-dimensional manifold usually appeals to the orientation of this manifold. We discuss how to avoid it constructing similar homotopy invariants of links in non-orientable manifolds.

Related

• Linking number in a projective space as the degree of a map
• Self-linking number of a real algebraic link
• Linking and coincidence invariants
• A Proof of the Invariant Based Formula for the Linking Number and its Asymptotic Behaviour
• Milnor's invariants for knots and links in closed orientable 3-manifolds