Cattaneo
Fakultäten » Mathematisch-naturwissenschaftliche Fakultät » Mathematik, Institut für » Reine Mathematik » Prof. Dr. Alberto Cattaneo » Cattaneo
Completed research project
| Title / Titel | Integral Invariants of Knots and Manifolds. Loop and Path Spaces and Topological BF Theories. Deformation Quantization and Poisson Sigma Models. | ||
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| Abstract (PDF, 14 KB) | |||
| Summary / Zusammenfassung | BF theories are generalizations of Chern-Simons theory that can be defined in any dimension. A spin-off of their perturbative quantization is the construction of cohomology classes of spaces of embedded circles and of higher-dimensional knot invariants. At the classical level they are related to Chas and Sullivan's string topology. |
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| Publications / Publikationen | Topological BF theories in 3 and 4 dimensions, J. Math. Phys. 36 (1995), 6137-6160 (with P. Cotta-Ramusino, J. Fröhlich and M. Martellini).Loop and path spaces and four-dimensional BF theories: connections, holonomies and observables, Commun. Math. Phys. 204 (1999), 493-524 (with P. Cotta-Ramusino and M. Rinaldi).Higher-dimensional BF theories in the Batalin-Vilkovisky formalism: the BV action and generalized Wilson loops, Commun. Math. Phys.221 (2001), 591-657 (with C. A. Rossi).Topological Field Theory Interpretation of String Topology, Commun. Math. Phys. 240 (2003), 397-421 (with J. Fröhlich and B. Pedrini).Wilson surfaces and higher dimensional knot invariants, Commun. Math. Phys. 256 (2005), 513-537 (with C. A. Rossi).Weitere Informationen | ||
| Project leadership and contacts / Projektleitung und Kontakte |
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| Funding source(s) / Unterstützt durch |
SNF (Personen- und Projektförderung) |
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| In collaboration with / In Zusammenarbeit mit |
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| Duration of Project / Projektdauer | Apr 2003 to Mar 2005 |