417 citations · 2.4k across the 99 of their papers we have counts for
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A note on the -invariant of 3-manifolds
Alberto S. Cattaneo, Tatsuro Shimizu
In this note, we revisit the -invariant as defined by R. Bott and the first author. The -invariant is an invariant of rational homology 3-spheres with acyclic orthogonal loca…
Split Chern-Simons theory in the BV-BFV formalism
Alberto S. Cattaneo, Pavel Mnev, Konstantin Wernli
The goal of this note is to give a brief overview of the BV-BFV formalism developed by the first two authors and Reshetikhin in [arXiv:1201.0290], [arXiv:1507.01221] in order to pe…
Algebraic structures on graph cohomology
Alberto S. Cattaneo, Paolo Cotta-Ramusino, Riccardo Longoni
We define algebraic structures on graph cohomology and prove that they correspond to algebraic structures on the cohomology of the spaces of imbeddings of S^1 or R into R^n. As a c…
Topological Field Theory Interpretation of String Topology
Alberto S. Cattaneo, Juerg Froehlich, Bill Pedrini
The string bracket introduced by Chas and Sullivan [math.GT/9911159] is reinterpreted from the point of view of topological field theories in the Batalin-Vilkovisky or BRST formali…
Configuration space integrals and invariants for 3-manifolds and knots
Alberto S. Cattaneo
The first part of this paper is a short review of the construction [dg-ga/9710001] of invariants of rational homology 3-spheres and knots in terms of configuration space integrals.…
Configuration spaces and Vassiliev classes in any dimension
Alberto S. Cattaneo, Paolo Cotta-Ramusino, Riccardo Longoni
The real cohomology of the space of imbeddings of S^1 into R^n, n>3, is studied by using configuration space integrals. Nontrivial classes are explicitly constructed. As a by-produ…