This Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences (CFDA 47.049) program provides funding of $226,665 to the University of Virginia (UVA) for research focused on the geometric classification and topological properties of 4-dimensional manifolds. The objectives include examining the validity of 4-dimensional topological surgery theory, studying symmetries of 4-dimensional spaces, and developing new tools for distinguishing them. The project aims to advance fundamental knowledge in geometry and topology, with potential applications in physics. Key research activities include investigating derived link invariants and using pseudo-isotopy methods to study mapping class groups of 4-manifolds. The award will also support research opportunities for undergraduate students, graduate students, and postdoctoral fellows, as well as outreach to middle school students. The funding is provided for the project period from June 1, 2024 to May 31, 2027.
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