SciPost Phys. 13, 071 (2022) ·
published 28 September 2022
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The cobordism conjecture of the swampland program states that the bordism
group of quantum gravity must be trivial. We investigate this statement in
several directions, on both the mathematical and physical side. We consider the
Whitehead tower construction as a possible organising principle for the
topological structures entering the formulation of the conjecture. We discuss
why and how to include geometric structures in bordism groups, such as higher
U(1)-bundles with connection. The inclusion of magnetic defects is also
addressed in some detail. We further elaborate on how the conjecture could
predict Kaluza--Klein monopoles, and we study the gravity decoupling limit in
the cobordism conjecture, with a few observations on NSNS string backgrounds.
We end with comments in relation to T-duality, as well as the finiteness
conjecture.
