nLab Konrad Waldorf

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Selected writings

On higher parallel transport in principal 2-bundles (nonabelian bundle gerbes) with 2-connection:

• Urs Schreiber, Konrad Waldorf, Smooth Functors and Differential Forms, Homology, Homotopy Appl., 13 1 (2011) 143-203 [arXiv:0802.0663, hha:1311953350]

• Urs Schreiber, Konrad Waldorf, Connections on nonabelian gerbes and their holonomy, Theory Appl. Categ. 28 17 (2013) 476-540 [arXiv:0808.1923, tac:28-17]

• Konrad Waldorf, Parallel transport in principal 2-bundles, Higher Structures 2 1 (2018) 57-115 [arXiv:1704.08542, pdf]

On bundle gerbes over Lie groups:

• Christoph Schweigert, Konrad Waldorf, Gerbes and Lie Groups, In: K. H. Neeb, A. Pianzola (eds.) Developments and Trends in Infinite-Dimensional Lie Theory, Progress in Mathematics, vol 288. Birkhäuser (2011) [arXiv:0710.5467, doi:10.1007/978-0-8176-4741-4_10]

Characterizing the image of the transgression operation from bundle gerbes (with connection) to complex line bundles (with connection) on the free loop space of their base space as consisting of fusion bundles:

• Konrad Waldorf, Transgression to Loop Spaces and its Inverse, I: Diffeological Bundles and Fusion Maps, Cah. Topol. Geom. Differ. Categ., 2012, Vol. LIII, 162-210 [arXiv:0911.3212, cahierstgdc:LIII]

• Konrad Waldorf, Transgression to Loop Spaces and its Inverse, II: Gerbes and Fusion Bundles with Connection, Asian Journal of Mathematics 20 1 (2016) 59-116 [arXiv:1004.0031, doi:10.4310/AJM.2016.v20.n1.a4]

• Konrad Waldorf, Transgression to Loop Spaces and its Inverse, III: Gerbes and Thin Fusion Bundles, Advances in Mathematics 231 (2012) 3445-3472 [arXiv:1109.0480, doi:10.1016/j.aim.2012.08.016]

On T-folds via principal 2-bundles for the T-duality 2-group:

• Thomas Nikolaus, Konrad Waldorf, Higher geometry for non-geometric T-duals, Commun. Math. Phys. 374 (2020) 317-366 [arXiv:1804.00677, doi:10.1007/s00220-019-03496-3]

On a smooth open/closed functorial field theory exhibiting the string‘s WZW term in a background with D-branes:

• Severin Bunk, Konrad Waldorf, Transgression of D-branes, Adv. Theor. Math. Phys. 25 5 (2021) 1095-1198 [arXiv:1808.04894, doi:10.4310/ATMP.2021.v25.n5.a1]

• Severin Bunk, Konrad Waldorf, Smooth functorial field theories from B-fields and D-branes, J. Homot. Rel. Struc. 16 1 (2021) 75-153 [doi:10.1007/s40062-020-00272-2, arXiv:1911.09990]

On geometric T-duality:

• Konrad Waldorf: Geometric T-duality: Buscher rules in general topology, Ann. Henri Poincaré 25 (2024) 1285–1358 [arXiv:2207.11799, doi:10.1007/s00023-023-01295-0]

On 2-vector bundles for 2-vector spaces regarded (here) as algebras with bimodules between them:

• Peter Kristel, Matthias Ludewig, Konrad Waldorf, The insidious bicategory of algebra bundles [arXiv:2204.03900]

On 2-representations of the string 2-group on 2-vector spaces and the construction of the stringor bundle:

• Peter Kristel, Matthias Ludewig, Konrad Waldorf, A representation of the string 2-group, [arXiv:2206.09797]

Reviewed in:

• Konrad Waldorf, The stringor bundle, talk at QFT and Cobordism, CQTS (Mar 2023) [web, video:YT]

Construction of the Connes fusion-operation on fibers of stringor bundles:

• Peter Kristel, Konrad Waldorf: Connes fusion of spinors on loop space, Compositio Mathematica 160 7 (2024) 1596-1650 [arXiv:2012.08142, doi:10.1112/S0010437X24007188]

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