On relating topological K-theory and, maybe, elliptic cohomology (at least the Witten genus) to functorial quantum field theory:
Stefan Stolz, Peter Teichner, Supersymmetric field theories and generalized cohomology, in: Hisham Sati, Urs Schreiber (eds.), Mathematical foundations of Quantum field theory and String theory, Proceedings of Symposia in Pure Mathematics, Volume 83, AMS (2011)
On supermanifolds from the point of view of functorial geometry:
Henning Hohnhold, Stephan Stolz, Peter Teichner: Super manifolds: an incomplete survey, Bulletin of the Manifold Atlas (2011) 1-6 [webpage, pdf, pdf]
Henning Hohnhold, Matthias Kreck, Stephan Stolz, Peter Teichner, Sections 2-3 of: Differential forms and 0-dimensional supersymmetric field theories, Quantum Topology Volume 2, Issue 1 (2011) pp. 1–41 (doi:10.4171/QT/12)
On slice knots:
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