Carlo Petronio's research activity


Main research interest: Three-dimensional topology

Current research topics:

Previous research topics:

Published papers and books:

(reprints/preprints of papers available upon request)
  1. Holomorphic automorphism groups in certain compact operator spaces
    Rendiconti Lincei, Matematica e Applicazioni (Serie IX) 1 (1990), 125-130.

  2. Holomorphic automorphisms of the unit ball of a direct sum
    Rendiconti Lincei, Matematica e Applicazioni (Serie IX) 1 (1990), 203-213.

  3. Direct Sums of Cartan Factors
    Rendiconti del Seminario Matematico dell'Universita` di Padova, 88 (1992), 111-125.

  4. (with R. Benedetti) Lectures on Hyperbolic Geometry
    Springer-Verlag, Berlin-Heidelberg-New York, 1992.

  5. An algorithm producing hyperbolicity equations for a link complement in S^3
    Geometriae Dedicata 44 (1992), 67-104.

  6. On Thurston's solitaire tilings of the plane
    Rend. Ist. Mat. Univ. Trieste 26 (1994),261-295.

  7. (With D. B. A. Epstein) An exposition of Poincaré's polyhedron theorem
    Enseign. Math. 40 (1994), 113-170.

  8. Standard spines and 3-manifolds
    Collana Tesi di Perfezionamento, Scuola Normale Superiore, Pisa, 1995 (1972K PS file or 693K uuencoded version available).

  9. (With R. Benedetti) A finite graphic calculus for 3-manifolds
    Manuscripta Mathematica 88 (1995), 291-310.

  10. (With R. Benedetti) On Roberts' proof of the Turaev-Walker theorem
    Journal of Knot Theory and its Ramifications 5 (1996), 427-439.

  11. Ideal triangulations of link complements and hyperbolicity equations
    Geometriae Dedicata 66 (1997), 27-50.

  12. (With R. Benedetti) Branched standard spines of 3-manifolds
    Lecture Notes in Math. 1653, Springer-Verlag, Berlin-Heidelberg-New York, 1997.

  13. (With C. de Fabritiis) Esercizi svolti e complementi di Topologia e Geometria
    Bollati-Boringhieri, Torino, 1997.

  14. A combinatorial approach to 3-manifolds
    Rendiconti del Circolo Matematico di Palermo, Serie II, Suppl. 49 (1997), 177-186.

  15. A Theorem of Eliashberg and Thurston on foliations and contact structures
    Scuola Normale Superiore, Pisa, 1997 (604K PS file or 290K uuencoded version available).

  16. (With R. Benedetti) Branched standard spines and contact structures on 3-manifolds
    Ann. Mat. Pura Appl. 178 (2000), 81-102 (833K PS file or 291K uuencoded version available).

  17. A note on codimension-1 foliations
    Rend. Sem. Mat. Univ. Padova 101 (1999), 137-145 (153K PS file or 85K uuencoded version available).

  18. (With J. R. Weeks) Partially flat ideal triangulations of cusped hyperbolic 3-manifolds
    Osaka J. Math. 37 (2000), 453-466 (1032K PS file or 226K uuencoded version available).

  19. (With J. Porti) Negatively Oriented Ideal Triangulations and a Proof of Thurston's Hyperbolic
    Dehn Filling Theorem
    Expositiones Mathematicae 18 (2000), 1-35 (764K PS file or 239K uuencoded version available).

  20. (With R. Benedetti) Reidemeister-Turaev Torsion of 3-Dimensional Euler Structures with
    Simple Boundary Tangency and Pseudo-Legendrian Knots
    Manuscripta Math. 106 (2001), 13-74 (2371K PS file or 563K gzipped version available).

  21. Ideal triangulations of hyperbolic 3-manifolds
    Atti del Sedicesimo congresso Dell'Unione Matematica Italiana, 593-608 (629K PS file or 192K uuencoded version available).

  22. (With N. Cucurachi) L'accertamento del rapporto di paternita' in assenza della madre
    Rivista Italiana di Medicina Legale 20 (2000), 1161-1173.

  23. (With R. Benedetti) Combed 3-manifolds with concave boundary, framed links, and pseudo-Legendrian links
    J. Knot Theory Ramifications 10 (2001), 1-35 (1694K PS file or 661K uuencoded version available).

  24. (With R. De Pietri) Feynman diagrams of generalized matrix models and the associated manifolds in dimension 4
    J. Math. Phys. 41 (2000), 6671-6688 (1546K PS file or 379K uuencoded version available).

  25. (With B. Martelli) 3-manifolds having complexity at most 9
    Experimental Math. 10 (2001), 207-237 (2740K PS file or 732K gzipped version available).

  26. (With R. Benedetti and J. Weeks) Compact 3-manifolds of negative curvature
    Proceedings of the IX Marcel Grossman Meeting, Rome, July 2-7, 2000, 2019-2022 (152K PS file available).

  27. (With G. Amendola, R. Benedetti and F. Costantino) Branched spines of 3-manifolds and torsion of Euler structures
    Rend. Ist. Mat. Univ. Trieste 32 (2001), 1-33, special volume dedicated to the memory of Marco Reni (943K PS file or 323K gzipped version available).

  28. (With B. Martelli) A new decomposition theorem for 3-manifolds
    Illinois J. Math. 46 (2002), 755-780 (760K PS file available).

  29. (With R. Frigerio) Construction and recognition of hyperbolic 3-manifolds with geodesic boundary
    Trans. Amer. Math. Soc. 356 (2004), 3243-3282 (550K PS file available).

  30. (With B. Martelli) Dehn filling of the `magic' 3-manifold
    Commun. Anal. Geom. 14 (2006), 969-1026 (1095K PS file available).

  31. (With B. Martelli) Complexity of geometric 3-manifolds
    Geom. Dedicata 108 (2004), 15-69 (971K PS file available).

  32. (With R. Frigerio and B. Martelli) Complexity and Heegaard genus of an infinite class of compact 3-manifolds
    Pacific J. Math. 210 (2003) 283-297 (481K PS file available).

  33. (With R. Frigerio and B. Martelli) Small hyperbolic 3-manifolds with geodesic boundary
    Experiment. Math. 13 (2004), 171-184 (371K PS file available).

  34. (With R. Frigerio and B. Martelli) Dehn filling of cusped hyperbolic 3-manifolds with geodesic boundary
    J. Differential Geom. 64 (2003), 425-455 (621K PS file available).

  35. (With F. Costantino, R. Frigerio and B. Martelli) Triangulations of 3-manifolds, hyperbolic relative handlebodies, and Dehn filling
    Comment. Math. Helv. 82 (2007), 903-944.

  36. Spherical splitting of 3-orbifolds,
    Math. Proc. Cambridge Philos. Soc. 142 (2007), 269-287.

  37. Complexity of 3-orbifolds,
    Topology Appl. 153 (2006), 1658-1681.

  38. (With Alexander Mednykh) Hyperbolic 3-manifolds with geodesic boundary: Enumeration and volume calculation,
    Proc. Steklov Inst. Math. 252 (2006), 155-171.

  39. (With Ekaterina Pervova) Complexity and T-invariant of Abelian and Milnor groups, and complexity of 3-manifolds,
    Math. Nachr. 281 (2008), 1182-1195.

  40. (With Ekaterina Pervova) On the existence of branched coverings between surfaces with prescribed branch data, I,
    Algebr. Geom. Top. 6 (2006), 1957-1985.

  41. (With Ekaterina Pervova) On the Hurwitz existence problem,
    Sib. Electron. Math. Izv. 2 (2005), 204-205.

  42. (With Sergei Matveev and Andrei Vesnin) Two-sided asymptotic bounds for the complexity of some closed hyperbolic three-manifolds,
    J. Aust. Math. Soc. 86 (2009), 205-219.

  43. (With Sergei Matveev and Andrei Vesnin) Two-sided complexity bounds for Lobell manifolds,
    Dokl. Akad. Nauk 416 (2007), 295-297, English translation in Dokl. Math. 76 (2007), 689-691.

  44. (With Ekaterina Pervova) On the existence of branched coverings between surfaces with prescribed branch data, II
    J. Knot Theory Ramifications 17 (2008), 787-816.

  45. (With Andrei Vesnin) Two-sided asymptotic bounds for the complexity of cyclic branched coverings of two-bridge links,
    Osaka J. Math. 46 (2009), 1077-1095.

  46. (With Damian Heard, Craig Hodgson and Bruno Martelli) Hyperbolic graphs of small complexity,
    Experiment. Math. 19 (2010), 211-236.

  47. Topologia dei nodi
    In: ``Immagini in Opera: Nuove Vie in Antropologia dell'Arte'', Guido Liguori, Napoli, 2007, pp. 265-292.

  48. (With Elisa Giusti, Marco Martorella, Fabrizio Berizzi)
    Equivalence between Cameron's Unit Disc and Poincaré's Half-Sphere for Symmetric Scattering Characterisation and Classification
    IEEE Geoscience and Remote Sensing Letters 5/2 (2008), 152-156.

  49. Combinatorial and geometric methods in topology
    (with an appendix by Damian Heard and Ekaterina Pervova),
    Milan Journal of Mathematics 76 (2008), 69-92.

  50. (With Damian Heard and Ekaterina Pervova) The 191 orientable octahedral manifolds
    Experiment. Math. 17 (2008), 473-486.

  51. (With Ekaterina Pervova) Realizability and exceptionality of candidate surface branched covers: methods and results
    Seminari di Geometria 2005-2009, Università degli Studi di Bologna, Dipartimento di Matematica, Bologna 2010, pp. 105-120.

  52. (With Maria Antonietta Pascali) Surface branched covers and geometric 2-orbifolds
    Trans. Amer. Math. Soc. 361 (2009), 5885-5920.

  53. (With Ekaterina Pervova) On colored Turaev-Viro invariants for knots in arbitrary 3-manifolds
    Int. Math. Res. Notices. IMRN (2009), 2547-2587.

  54. (With Ekaterina Pervova) Complexity of links in 3-manifolds,
    J. Knot Theory Ramif. 18 (2009), 1439-1458.

  55. (With Pietro Corvaja and Umberto Zannier) On certain permutation groups and sums of two squares,
    Elem. Math. 67 (2012), 169-181.

  56. Algorithmic construction and recognition of hyperbolic 3-manifolds, links, and graphs,
    In "Strasbourg Master Class on Geometry" (A. Papadopoulos, ed.), European Mathematical Society, 2012, pp. 371-404.

  57. (With Maria Antonietta Pascali) Branched covers of the sphere and the prime-degree conjecture,
    Ann. Mat. Pura Appl. 191 (2012), 563-594.

  58. (With Ekaterina Pervova and Vito Sasso) Notes on the complexity of 3-valent graphs in 3-manifolds,
    J. Knot Theory Ramif. 21, 1250085 (2012) [12 pages] DOI: 10.1142/S021821651250085X.

  59. (with Bruno Martelli and Fionntan Roukema) Exceptional Dehn surgery on the minimally twisted five-chain link,
    Commun. Anal. Geom. 22 (2014), 689-735.

  60. (with Michele Tocchet) Notes on the peripheral volume of hyperbolic 3-manifolds,
    Math. Nachr. 287 (2014), 677-685.

  61. (with Riccardo Benedetti) Spin structures on 3-manifolds via arbitrary triangulations,
    Algebr. Geom. Topol. 14 (2014), 1005-1054.

  62. Generic flows on 3-manifolds,
    Kyoto J. Math. 55 (2015), 143-167.

  63. (with Adolfo Zanellati) Algorithmic simplification of knot diagrams: new moves and experiments,
    J. Knot Theory Ramifications 25 (2016), Article ID 1650059, 30 p.

  64. (with Tom Ferragut) Elementary solution of an infinite sequence of instances of the Hurwitz problem,
    Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl. 29 (2018), 297-307.

  65. Explicit computation of some families of Hurwitz numbers,
    European J. Combin. 75 (2019), 136-151.

  66. (with Luciano Modica) "Il teorema più bello",
    Pisa University Press, 2018.

  67. Explicit computation of some families of Hurwitz numbers, II,
    arXiv:1807.11067, to appear in Adv. Geom.

  68. (with Filippo Sarti) Counting surface branched covers,
    arXiv:1901.08316, to appear in Studia Sci. Math. Hungar.

  69. Realizations of certain odd-degree surface branch data,
    arXiv:1903.10866, submitted.