Higher order linking numbers, curvature and holonomy

Mauro Spera, Vittorio Penna

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)


A differential geometric approach to Milnor-Massey higher order linking numbers for generic links is devised, via Chen's theory of iterated path integrals. Massey linking numbers arise from curvature forms of nilpotent "topological" connections, determined by the link structure, and interpreted in terms of intersection theory, leading to a fairly easy computation thereof. A version of the Turaev-Porter theorem expressing equality of Milnor and Massey linking numbers is also exhibited along the same lines, by computing suitable flat connection parallel transport operators in two different ways.
Original languageEnglish
Pages (from-to)701-723
Number of pages23
JournalJournal of Knot Theory and its Ramifications
Publication statusPublished - 2002


  • higher order linking numbers, Chen integrals, nilpotent connections


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