Generalized Bott–Cattaneo–Rossi invariants of high-dimensional long knots

Abstract

Bott, Cattaneo and Rossi defined invariants of long knots ℝ^𝑛 ↪ ℝ^𝑛+2 as combinations of configuration space integrals for 𝑛 odd ≥ 3. Here, we give a more flexible definition of these invariants. Our definition allows us to interpret these invariants as counts of diagrams. It extends to long knots inside more general (𝑛 + 2)-manifolds, called asymptotic homology ℝ^𝑛+2, and provides invariants of these knots.