- R. Hoekzema, M. Merling, L. Murray, C. Rovi, J. Semikina
"Cut and paste invariants of manifolds via algebraic K-theory".
Accepted for publication
arXiv link - D. Benson, C. Campagnolo, A. Ranicki, C. Rovi
"Cocycles on the mapping class group and the symplectic groups".
Accepted for publication
arXiv link - C. Rovi, M. Schoenbauer
"Relating Cut and Paste Invariants and TQFTs".
Results from REU summer program 2017. Accepted for publication
arXiv link - D. Benson, C. Campagnolo, A. Ranicki, C. Rovi
"Cohomology of symplectic groups and Meyer's signature theorem".
Algebraic & Geometric topology, Vol. 18, Issue 7 (2018), 4069-4091
arXiv link - C. Rovi
"The non-multiplicativity of the signature modulo $8$ of a fibre bundle is an Arf-Kervaire invariant". Algebraic & Geometric Topology, Vol. 18, Issue 3 (2018) 1281 - 1322
arXiv link - C. Rovi & S. Yokura
"Hirzebruch $\chi_y$-genera modulo $8$ of fiber bundles for odd integers $y$
Pure and Applied Mathematics Quarterly, Vol. 12, No. 4 (2016), pp. 587-602.
arXiv link - C. Rovi
"The Signature modulo 8 of Fibre Bundles". PhD Thesis, Edinburgh 2015.
arXiv link - V. Coufal, D. Pronk, C. Rovi, L. Scull, C. Thatcher.
"Orbispaces and their Mapping Spaces via Groupoids: A Categorical Approach". Contemporary Mathematics: Women in Topology: Collaborations in Homotopy theory. Vol 641. Providence, RI: American Mathematical Society, 2015.
arXiv link
AMS Journal link - J. Davis, C. Rovi.
"The reinterpretation of Davis-Lueck equivariant homology in terms of $L$-theory".
In preparation - J. Davis, C. Rovi.
"A proof of the $L$-theoretic Farrell-Jones conjecture for semidirect products with the infinite cyclic group".
In preparation - B. Riley, C. Rovi.
"Cut paste operations and bordism in an equivariant setting".
Results from REU summer program 2018.
In preparation. Draft available upon request
Research Interests
My research interests are in Algebraic topology: surgery theory, topology of manifolds and K- and L-theory. I am also interested in TQFTs.
My research interests include Surgery theory and K-theory.
I am interested in using an algebraic approach to obtaining new
information about geometric properties of manifolds and about quadratic forms. This information
is obtained by studying certain invariants, specially the signature invariant which is
key to my research project. This project lies at the crossroads between surgery theory and algebraic
K-theory and it seeks to explore the behaviour of the signature invariant in the context of
fibre bundles. The divisibility of the signature by higher powers of 2 is a key to understanding
the relationship between manifolds and higher algebraic K-theory: divisibility by 2 is
detected by the Euler characteristic, divisibility by 4 by Whitehead torsion, divisibility by
8 by the K2-valued Hasse invariant. What next? Atiyah pointed out that finding
non-trivial signatures in the context of fibre bundles is closely related to the problem of the
construction of Topological Quantum Field Theories (TQFTs). The goal of my project is to
gain a better understanding of the obstructions to divisibility of the signature specially in
the context of fibre bundles.
My research statement can be found here.
A lay version of the research statement can be found here.