On the Homological Stability of Orthogonal and Spin Groups

Lead Research Organisation: University of Warwick
Department Name: Mathematics


In this project, we have proven homological stability results for the split orthogonal group O_{n,n}; the special split orthogonal group SO_{n,n} and the Spin group Spin_{n,n}. We conjecture that our results are optimal, by conjecturing the obstruction to further homological stability, in the form of the relative homology groups. We have low dimensional computations that support our conjecture.

Specifically, it is conjectured that these obstructions are related to Milnor K-Theory and Milnor-Witt K-Theory. Therefore, if these conjectures are true, there would exist a connection between the homology of these groups and K-Theory. In particular, for the Spin groups, this would provide a beautiful connection between a concept originating from Particle Physics and Milnor-Witt K-Theory; a concept originating from Motivic Homotopy Theory.


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Studentship Projects

Project Reference Relationship Related To Start End Student Name
EP/V520226/1 30/09/2020 31/10/2025
2443761 Studentship EP/V520226/1 04/10/2020 04/10/2024 Sunny Sood