


 Joao Faria Martins, Frank W Nijhoff, Daniel Riccombeni: The DarbouxKP system as an integrable ChernSimons multiform theory in infinite dimensional space. arXiv:2305.03182 [mathph]
 Faria Martins J, Porter T : A categorification of Quinn's finite total homotopy TQFT with application to TQFTs and onceextended TQFTs derived from strict omegagroupoids. arXiv:2301.02491 [math.CT]. (235 pages, preliminary version.)
 Koppen V, Faria Martins J,
Martin
P: Exactly solvable models for 2+1D topological phases derived from crossed modules of semisimple Hopf algebras. arXiv:2104.02766 [mathph]
Publications (comments are very welcome as well):
 Motion groupoids and mapping class groupoids. arXiv:2103.10377 [mathph], with Fiona Torzewska and Paul Martin. To appear in Commmunications in Mathematical Physics.
On a canonical lift of Artin's representation to loop braid groups. With Celeste Damiani and Paul Martin. Journal of Pure and Applied Algebra Volume 225, Issue 12, December 2021, 106760. Preliminary version.
Representations of the Loop Braid Group and AharonovBohm like effects in discrete (3+1)dimensional higher gauge theory. With Alex Bullivant and Paul Martin. Advances in Theoretical and Mathematical Physics.(To appear.)
Preliminary version.
Higher lattices, discrete twodimensional holonomy and topological phases in (3+1) D with higher gauge symmetry. With Alex Bullivant, Marcos Calçada,
Zoltán Kádár and Paul Martin. Reviews in Mathematical Physics, Vol. 32, No. 04, 2050011 (2020) Research Paper. Postprint version. Earlier version (arXiv:1702.00868 [mathph]).
Topological phases from higher
gauge symmetry in 3+1D. With Alex Bullivant, Marcos Calçada,
Zoltán Kádár and Paul Martin. PHYSICAL REVIEW B 95, 155118 (2017). Preliminary version.
Categorifying the $sl(2,C)$ KnizhnikZamolodchikov Connection via an
Infinitesimal 2YangBaxter Operator in the String Lie2Algebra,
with
Lucio Simone Cirio. Advances in Theoretical and Mathematical Physics. Volume 21 (2017)
Number 1, Pages: 147  229.
Preliminary version.
Crossed modules of Hopf algebras and of associative algebras and twodimensional holonomy.
Journal of Geometry and Physics. Volume 99, January 2016, Pages 68110
Preliminary version.
TwoFold Homotopy of 2Crossed
Module Maps of Commutative Algebras. With İ.İlker Akça and Kadir Emir. Communications in Algebra 47 (2019), no. 1, 289–311. Preliminary version.
Pointed Homotopy of Maps Between 2Crossed Modules of Commutative Algebras, with İ.İlker Akça and Kadir Emir. Homology,
Homotopy and Applications18 (2016), no. 1, 99–128. Preliminary version.
Link invariants from finite categorical groups, with Roger
Picken. Homology, Homotopy & Applications. 2015, Vol. 17 Issue 2, p205233. 29p. Preliminary version. This is a very reduced version of: Link invariants from finite categorical groups and braided crossed modules.
Infinitesimal 2braidings and differential crossed modules, with Lucio Cirio.
Advances in Mathematics,
Volume 277, 4 June 2015, Pages 426–491. Preliminary version.
Pointed homotopy and pointed lax homotopy of 2crossed module maps,
with Björn Gohla, Advances in Mathematics
Volume 248, 25 November 2013, Pages 986–1049. Preliminary version. Very preliminary version.
Spin Foam State Sums and ChernSimons Theory, with Aleksandar
Miković . ChernSimons gauge theory: 20 years after, 277–284, AMS/IP Stud. Adv. Math., 50, Amer. Math. Soc., Providence, RI, 2011.
Preliminary version.
Categorifying the Knizhnik–Zamolodchikov connection,
with
Lucio Simone Cirio, Differential Geometry and its Applications, Volume 30, Issue 3, June 2012, Pages 238–261. Preliminary version.
FourDimensional Spin Foam Perturbation Theory, with Aleksandar
Miković .
Symmetry, Integrability and Geometry: Methods and Applications (SIGMA).
7 (2011), 094, 22 pages.
The fundamental 2crossed complex of a reduced CWcomplex.
Homology,
Homotopy and Applications, Vol. 13 (2011), No. 2, pp.129157.
Lie crossed modules and gaugeinvariant actions for 2BF theories, with Aleksandar Miković. Advances in Theoretical and Mathematical Physics, Volume 15, Number 4 (August 2011) p.10591084. Preliminary version
Surface
Holonomy for NonAbelian 2Bundles via Double Groupoids, with
Roger Picken.
Advances
in Mathematics
Volume
226, Issue 4, 1 March 2011, Pages 33093366. Preliminary version.
Very preliminary version.
The
fundamental Gray 3groupoid of a smooth manifold and local
3dimensional holonomy based on a 2crossed module, with Roger
Picken. Differential
Geometry and its Applications Volume
29, Issue 2, March 2011, Pages 179206. Preliminary version. Very preliminary version.
On
TwoDimensional Holonomy, with Roger
Picken. Transactions of the
American Mathematical Society, 362 (2010), 56575695.
Spin
Foam Perturbation Theory for ThreeDimensional Quantum Gravity,
with Aleksandar
Miković . Communications
in Mathematical Physics. Volume 288, Number 2 / June,
2009.
The
Fundamental Crossed Module of the Complement of a Knotted Surface.
Transactions of the American
Mathematical Society. 361 (2009), 45934630.
Invariants
of Welded Virtual Knots Via Crossed Module Invariants of Knotted
Surfaces, with Louis
H. Kauffman. Compositio
Mathematica. Volume 144, Issue 04, July 2008, pp
10461080.
Invariants
of Spin Networks Embedded in ThreeManifolds,
with Aleksandar
Miković. Communications
in Mathematical Physics, Volume 279, Number 2/ Abril
2008, pages 381399.
Observables
in the TuraevViro and CraneYetter models, with John
W. Barrett and J. Manuel Garcia Islas. Journal
of Mathematical Physics, 48, 093508 (2007) (18
pages).
On
Yetter's Invariant and an Extension of the DijkgraafWitten Invariant
to Categorical Groups, with Timothy
Porter. Theory and
Application of Categories, Vol. 18, 2007, No. 4, pp 118150.
On the
Homotopy Type and the Fundamental Crossed Complex of the Skeletal
Filtration of a CWComplex. Homology
Homotopy and Applications, Vol. 9
(2007), No. 1, pp.295329.
Categorical
Groups, Knots and Knotted Surfaces, J.
Knot Theory Ramifications 16 (2007), no 9, 11811217.
Other work:
On 2Dimensional Homotopy Invariants of Complements of Knotted Surfaces.
Note:
This is an archaic version of "The Fundamental Crossed Module of the Complement of a Knotted Surface, Trans AMS. 361 (2009), 45934630", using movies of knotted surfaces with bands and spanners rather than hyperbolic splittings of knotted surfaces for constructing a representation of the algebraic homotopy 2type of the complement of a knotted surface. May still be of interest.
PhD Thesis:
Quantum Topology and the Lorentz Group.