Categorical Smoothness of 4-Manifolds
  • quantum spacetime structure
  • exotic 4-smoothness
  • quantum mechanics
  • information loss
Video Introduction

This video is adapted from 10.3390/e24030391

If black holes leave empty spacetime after they evaporate, the information about quantum matter forming black hole is lost. This is the celebrated information paradox originally stated by Hawking. Researchers focus on some aspects of the relation of spacetime and quantum mechanics and the study counterparts (in Set) of the categorical local symmetries of smooth 4-manifolds. In the set-theoretic limit, there emerge some exotic smoothness structures on  R 4 (hence the Riemannian nonvanishing curvature), which fit well with the quantum mechanical lattice of projections on infinite-dimensional Hilbert spaces.

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Król, J.; Asselmeyer-Maluga, T. Categorical Smoothness of 4-Manifolds. Encyclopedia. Available online: (accessed on 24 April 2024).
Król J, Asselmeyer-Maluga T. Categorical Smoothness of 4-Manifolds. Encyclopedia. Available at: Accessed April 24, 2024.
Król, Jerzy, Torsten Asselmeyer-Maluga. "Categorical Smoothness of 4-Manifolds" Encyclopedia, (accessed April 24, 2024).
Król, J., & Asselmeyer-Maluga, T. (2022, August 22). Categorical Smoothness of 4-Manifolds. In Encyclopedia.
Król, Jerzy and Torsten Asselmeyer-Maluga. "Categorical Smoothness of 4-Manifolds." Encyclopedia. Web. 22 August, 2022.