# Cattaneo

### Completed research project

Title / Titel Integral Invariants of Knots and Manifolds
PDF Abstract (PDF, 14 KB)
Summary / Zusammenfassung Using configuration-space integrals and graph cohomology, it is possible to write several types of invariants; e.g.: Vassiliev's finite-type invariants of knots, invariants of rational homology 3-spheres, cohomology classes of the space of embedded circles in $$R^n$$. Our research concentrates on the study of the properties of these invariants and of the underlying graph complexes as well as on the extension of these techniques to other cases.
Publications / Publikationen Integral invariants of 3-manifolds, J. Diff. Geom. 48 (1998), 91-133 (with R. Bott).

Integral invariants of 3-manifolds. II, J. Diff. Geom. 53 (1998), 1-13 (with R. Bott).

Configuration spaces and Vassiliev classes in any dimension, Algebr. Geom. Topol. 2 (2002), 949-1000 (with P. Cotta-Ramusino and R. Longoni).

Algebraic structures on graph cohomology, J. of Knot Theory and Its Ramifications 14 (2005), 627-640 (with P. Cotta-Ramusino and R. Longoni).

Remarks on Chern-Simons Invariants
Commun. Math. Phys. 293 (2010), 803-836 (with P. Mnev)

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