nLab João Faria Martins

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Selected writings

On the relation between the Turaev-Viro model and the Crane-Yetter model:

• John Barrett, J. Garcia-Islas, João Faria Martins, Observables in the Turaev-Viro and Crane-Yetter models, J. Math. Phys. 48:093508, 2007 (arXiv:math/0411281)

On spin networks:

• João Faria Martins, Aleksandar Mikovic, Invariants of spin networks embedded in three-manifolds.

  Comm. Math. Phys. (2006) 279, pp. 381-399, (arXiv:gr-qc/0612137, doi:10.1007/s00220-008-0422-8)

On the Yetter invariant:

• João Faria Martins and Tim Porter, On Yetter’s invariant and an extension of the Dijkgraaf-Witten invariant to categorical groups, Theory and Applications of Categories, Vol. 18, 2007, No. 4, pp 118-150.

  (TAC)

On 2-crossed modules, 2-crossed complexes and the maps and homotopies between such:

• Joao Faria Martins, The fundamental 2-crossed complex of a reduced CW-complex, Homology Homotopy Appl. 13(2): 129-157 (2011) (web pdf.)

• Björn Gohla, João Faria Martins: Pointed homotopy and pointed lax homotopy of 2-crossed module maps, Advances in Mathematics, (248), (2013), Pages 986 - 1049, doi

On higher parallel transport in dimension 2 (connections on 2-bundles):

• João Faria Martins, Roger Picken: On 2-dimensional holonomy, Trans. Amer. Math. Soc. 362 (2010), 5657-5695 [arXiv:0710.4310, doi:10.1090/S0002-9947-2010-04857-3]

• João Faria Martins, Roger Picken: Surface holonomy for non-abelian 2-bundles via double groupoids, Advances in Mathematics 226 4 (2011) 3309-3366 [doi:10.1016/j.aim.2010.10.017]

and application to categorification of the Knizhnik-Zamolodchikov connection:

• Lucio Simone Cirio, João Faria Martins: Categorifying the Knizhnik–Zamolodchikov connection, Differential Geometry and its Applications 30 3 (2012) 238-261 [doi:10.1016/j.difgeo.2012.03.004, arXiv:1106.0042]

and to BFCG theory:

• João Faria Martins, Aleksandar Miković: Lie crossed modules and gauge-invariant actions for 2-BF theories, Adv. Theor. Math. Phys. 15 4 (2011) 913-1199 [arXiv:1006.0903, euclid:atmp/1339438351]

On motion groupoids and mapping class groups:

• Fiona Torzewska, João Faria Martins, Paul Purdon Martin, Motion groupoids and mapping class groupoids, Comm. Math. Phys. 402 (2023) 1621-1705 [arXiv:2103.10377, doi:10.1007/s00220-023-04755-0]

On Quinn’s finite homotopy field theory:

• João Faria Martins, Timothy Porter, A categorification of Quinn’s finite total homotopy TQFT with application to TQFTs and once-extended TQFTs derived from strict omega-groupoids [arXiv:2301.02491]

Related entries

• path n-groupoid

• principal 2-bundle

• 3-groupoid of Lie 3-algebra valued forms

• Yetter model

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