6 papers · 1 filter
Conformal Anomalies via Canonical Traces
S. Paycha, S. Rosenberg
Using Laurent expansions of the Kontsevich-Vishik canonical trace of holomorphic families of classical pseudodifferential operators, we define functionals on the space of Riemannia…
Infinite Dimensional Chern-Simons Theory
Steven Rosenberg, Fabian Torres-Ardila
We extend finite dimensional Chern-Simons theory to certain infinite dimensional principal bundles with connections, in particular to the frame bundle over the loop spa…
Chern-Weil Constructions on DO Bundles
Sylvie Paycha, Steven Rosenberg
We construct Chern-Weil classes on infinite dimensional vector bundles with structure group contained in the algebra $\cl[\leq 0](M, E)$ of non-positive order classical pseudo-diff…
Gauge Theory Techniques in Quantum Cohomology
S. Rosenberg, M. Vajiac
Quantum cohomology gives a finite dimensional integrable system via the Dubrovin connection. Motivated by Givental's work on mirror symmetry, we use gauge theory techniques and the…
Curvature on determinant bundles and first Chern forms
Sylvie Paycha, Steven Rosenberg
The Quillen-Bismut-Freed construction associates a determinant line bundle with connection to an infinite dimensional super vector bundle with a family of Dirac-type operators. We…
Mathai-Quillen forms and Lefschetz theory
Mihail Frumosu, Steven Rosenberg
Mathai-Quillen forms are used to give an integral formula for the Lefschetz number of a smooth map of a closed manifold. Applied to the identity map, this formula reduces to the Ch…