nLab Mathai Varghese (changes)

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Selected writings

On equivariant de Rham cohomology

• Varghese Mathai, Daniel Quillen, Superconnections, Thom classes and equivariant differential forms, Topology 25, 85 (1986) (doi:10.1016/0040-9383(86)90007-8)

On Early discussion of non-commutative orbifold geometry K-theory -deformation of via the self-dual $C^\ast$-algebras higher gauge theory as it appears on the M5-brane worldvolume, and its S-duality:

• Varghese Mathai ,

  Matilde Marcolli, Varghese Mathai: Twisted higher index theory on good orbifolds and fractional quantum numbers [[arXiv:math/9803051](https://arxiv.org/abs/math/9803051)]

  Hisham Sati , Higher abelian gauge theory associated to gerbes on noncommutative deformed M5-branes and S-duality, J. Geom. Phys. 92:240-251, 2015 (arXiv:1404.2257)

• Matilde Marcolli, Varghese Mathai: Twisted index theory on good orbifolds, I: noncommutative Bloch theory, Communications in Contemporary Mathematics 1 4 (1999) 553-587 [[arXiv:math/9911102v1](https://arxiv.org/abs/math/9911102), doi:10.1142/S0219199799000213]

• Matilde Marcolli, Varghese Mathai: Twisted higher index theory on good orbifolds, II: fractional quantum numbers, Commun. Math. Phys. 217 1 (2001) 55-87 [[arXiv:math/9911103](https://arxiv.org/abs/math/9911103), doi:10.1007/s002200000351]

On topological T-duality:

• Peter Bouwknegt, Jarah Evslin, Varghese Mathai, T-Duality: Topology Change from H-flux, Commun. Math. Phys. 249:383-415, 2004 (hep-th/0306062)

• Peter Bouwknegt, Keith Hannabus, Varghese Mathai, T-duality for principal torus bundles, JHEP 0403 (2004) 018 (hep-th/0312284)

• Varghese Mathai, Jonathan Rosenberg, T-Duality for Torus Bundles with H-Fluxes via Noncommutative Topology (arXiv:hep-th/0401168)

On the fractional quantum Hall effect via noncommutative geometry:

• Matilde Marcolli, Varghese Mathai: Towards the fractional quantum Hall effect: a noncommutative geometry perspective, in Noncommutative Geometry and Number Theory, Vieweg (2006) [doi:10.1007/978-3-8348-0352-8_12, arXiv:cond-mat/0502356]

On analytic torsion and twisted de Rham cohomology:

• Varghese Mathai, Siye Wu, Analytic torsion for twisted de Rham complexes, J. Diff. Geom. 88:297-332, 2011 (arXiv:0810.4204)

On non-commutative geometry-deformation of the self-dual higher gauge theory as it appears on the M5-brane worldvolume, and its S-duality:

• Varghese Mathai, Hisham Sati, Higher abelian gauge theory associated to gerbes on noncommutative deformed M5-branes and S-duality, J. Geom. Phys. 92 (2015) 240-251 [[arXiv:1404.2257](https://arxiv.org/abs/1404.2257)]

On a twisted equivariant version of the Bismut-Chern character:

• Fei Han, Varghese Mathai, Exotic twisted equivariant cohomology of loop spaces, twisted Bismut-Chern character and T-duality, Commun. Math. Phys. 337 (2015) 127-150 [[arXiv:1405.1320](https://arxiv.org/abs/1405.1320), doi:10.1007/s00220-014-2270-z]

reviewed in:

• Varghese Mathai, T-duality for loop spaces, or equivalently for the 1D sigma model, talk at M-Theory and Mathematics 2023, NYU Abu Dhabi (Jan 2023) [[web](/nlab/show/M-Theory+and+Mathematics#Mathai2023)]

On T-duality in the K-theory classification of topological phases of matter, related to the Fourier transform between crystals and their Brillouin torus:

• Varghese Mathai, Guo Chuan Thiang, T-Duality of Topological Insulators, J.Phys.A: Math. Theor. 48 (2015) 42FT02 [doi:10.1088/1751-8113/48/42/42FT02]

• Varghese Mathai, Guo Chuan Thiang: T-Duality Simplifies Bulk-Boundary Correspondence, Commun. Math. Phys. 345 (2016) 675–701 [doi:10.1007/s00220-016-2619-6, arXiv:1505.05250]

• Varghese Mathai, Guo Chuan Thiang, T-duality simplifies bulk-boundary correspondence: some higher dimensional cases, Annales Henri Poincaré 17 12 (2016) 3399-3424 [doi:10.1007/s00023-016-0505-6, arXiv:1506.04492]

• Keith C. Hannabuss, Varghese Mathai, Guo Chuan Thiang, T-duality trivializes bulk-boundary correspondence: the parametrised case, Adv. Theor. Math. Phys. 20 (2016) 1193-1226 [doi:10.4310/ATMP.2016.v20.n5.a8, arXiv:1510.04785]

• Keith C. Hannabuss, Varghese Mathai, Guo Chuan Thiang, T-duality simplifies bulk-boundary correspondence: the noncommutative case, Lett. Math. Phys. 108 5 (2018) 1163-1201 [doi:10.1007/s11005-017-1028-x, arXiv:1603.00116]

Aspects of the classification of semi-metals seen in ordinary cohomology:

• Varghese Mathai, Guo Chuan Thiang, Global topology of Weyl semimetals and Fermi arcs, J. Phys. A: Math. Theor. 50 (2017) 11LT01 (arXiv:1607.02242, doi:10.1088/1751-8121/aa59b2)

• Varghese Mathai, Guo Chuan Thiang, Differential Topology of Semimetals, Commun. Math. Phys. 355 (2017) 561–602, (arXiv:1611.08961, doi:10.1007/s00220-017-2965-z)

On the Witten genus:

• Fei Han, Varghese Mathai, Projective elliptic genera and elliptic pseudodifferential genera, Adv. Math. 358 (2019) 106860 (arXiv:1903.07035)

On spherical T-duality:

• Lachlan Macdonald, Varghese Mathai, Hemanth Saratchandran, On the Chern character in Higher Twisted K-theory and spherical T-duality (arXiv:2007.02507)

On bundle gerbe modules with higher G-structures (including String structure, etc.) and the corresponding twisted Chern character:

• Fei Han, Ruizhi Huang, Varghese Mathai, Fractional structures on bundle gerbe modules and fractional classifying spaces [[arXiv:2203.14439](https://arxiv.org/abs/2203.14439)]