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Differential homology and cohomology, gerbes and applications


The main part of this project concerns differential cohomology theories. The fundamental aim consists of completing the description of these theories and of the corresponding homology theories, underlining the analogy with ordinary cohomology, i.e. with the differential extension of singular cohomology. It is necessary to describe in the proper way the relative, twisted and equivariant versions, showing how each fundamental feature of ordinary cohomology can be generalized to a generic cohomology theory. This description may be interesting even because of the applications in mathematical physics, in particular to study the geometrical and topological foundations of string theory. The second part of the project concerns non-abelian topological gerbes. The main aim consists of trying to define Chern classes, starting from a conjecture about their structure. Moreover, via non-abelian gerbes it seems to be possible to define K-theory twisted by a class H whose degree is not necessarily 3, and this is the second aim. Finally, the project will be completed discussing some interesting topological problems that arose during my past research activity. The topics I will consider in the project are not studied up to now in the mathematics department of Ufscar, neither from a purely mathematical point of view, nor about the applications in mathematical physics. Hence, it could be an opportunity to develop some new research lines within the group of Geometry and Topology of Ufscar. (AU)

Scientific publications
(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)
RUFFINO, FABIO FERRARI; ROCHA BARRIGA, JUAN CARLOS. y Twisted differential K-characters and D-branes. Nuclear Physics B, v. 960, NOV 2020. Web of Science Citations: 0.
RUFFINO, FABIO FERRARI. Flat pairing and generalized Cheeger-Simons characters. Journal of Homotopy and Related Structures, v. 12, n. 1, p. 143-168, MAR 2017. Web of Science Citations: 1.

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