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.

Publications and Preprints

  1. 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

  2. D. Benson, C. Campagnolo, A. Ranicki, C. Rovi

    "Cocycles on the mapping class group and the symplectic groups".
    Submitted for publication
    arXiv link

  3. C. Rovi, M. Schoenbauer

    "Relating Cut and Paste Invariants and TQFTs".
    Results from REU summer program 2017. Submitted for publication
    arXiv link

  4. 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

  5. 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

  6. 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

  7. C. Rovi

    "The Signature modulo 8 of Fibre Bundles". PhD Thesis, Edinburgh 2015.
    arXiv link

  8. 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

  9. J. Davis, C. Rovi.

    "The reinterpretation of Davis-Lueck equivariant homology in terms of $L$-theory".
    In preparation

  10. J. Davis, C. Rovi.

    "A proof of the $L$-theoretic Farrell-Jones conjecture for semidirect products with the infinite cyclic group".
    In preparation

  11. 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

  12. 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.

  13. Notes

    1. 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.
    2. 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.