- R. Hoekzema, M. Merling, L. Murray, C. Rovi, J. Semikina
"Cut and paste invariants of manifolds via algebraic K-theory".
Submitted for publication
arXiv link - D. Benson, C. Campagnolo, A. Ranicki, C. Rovi
"Cocycles on the mapping class group and the symplectic groups".
Submitted for publication
arXiv link - C. Rovi, M. Schoenbauer
"Relating Cut and Paste Invariants and TQFTs".
Results from REU summer program 2017. Submitted 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 - J. Bergner, T-D. Bradley, B. Johnson, S. Raynor, C. Rovi, L. Wells.
"Direct proofs of properties and structures of model structures for $(\infty,1)$-categories".
In preparation. - My First year report:
"algebraic and geometric cutting and pasting of manifolds"
During my first year PhD I worked on cutting and pasting of manifolds. This idea grew out of a series of papers by Jaenich which studied the Novikov additivity of the signature. The cut and paste operation gives rise to different types of groups: the (Schneiden und Kleben) SK-groups, the bordism SK-groups and furthermore the SKK groups. The theory about these groups and their relation with cobordism theory was developed in Cutting and Pasting of Manifolds; SK-Groups by U.Karras, M.Kreck, W.D Neumann and E.Ossa.
- A note on SKK groups
The SKK groups are the SK-controlled groups. The SKK-groups where first defined by Karras, Kreck, Neumann and Ossa. During my first months in PhD I wrote a report on the definition of the SKK-groups, giving examples and relating them to the SK-groups. The SKK-group invariants have become relevant in the application to TQFTs developed recently by Matthias Kreck.
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.
My research is supported by an AMS-Simons travel grant.