6 citations · 16 across the 13 of their papers we have counts for
14 papers
Beyond the Space-Time Boundary
Michael Heller, Jerzy Król
In General Relativity a space-time is regarded singular if there is an obstacle that prevents an incomplete curve in to be continued. Usually, such a space-time is complete…
Gravity in the smallest
Michael Heller, Jerzy Król
Synthetic Differential Geometry (SDG) is a categorical version of differential geometry based on enriching the real line with infinitesimals and weakening of classical logic to int…
Synthetic Approach to the Singularity Problem
Michael Heller, Jerzy Król
We try to convince the reader that the categorical version of differential geometry, called Synthetic Differential Geometry (SDG), offers valuable tools which can be applied to wor…
How Logic Interacts with Geometry: Infinitesimal Curvature of Categorical Spaces
Michael Heller, Jerzy Król
In category theory, logic and geometry cooperate with each other producing what is known under the name Synthetic Differential Geometry (SDG). The main difference between SDG and s…
Model and Set-Theoretic Aspects of Exotic Smoothness Structures on
Jerzy Król
Model-theoretic aspects of exotic smoothness were studied long ago uncovering unexpected relations to noncommutative spaces and quantum theory. Some of these relations were worked…
Higgs potential and confinement in Yang-Mills theory on exotic R^4
Torsten Asselmeyer-Maluga, Jerzy Król
We show that pure SU(2) Yang-Mills theory formulated on certain exotic R^4 from the radial family shows confinement. The condensation of magnetic monopoles and the qualitative form…