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Transfer systems for rank two elementary abelian groups: characteristic functions and matchstick games
We develop the theory of saturated transfer systems on modular lattices, ultimately producing a “matchstick game” that puts saturated transfer systems in bijection with certain structured subsets of covering relations. We also prove that Hill’s characteristic function χ for transfer systems on a lattice P surjects onto interior operators for P, and moreover, the fibers of χ have unique maxima which are exactly the saturated transfer systems. Lastly, after an interlude developing a recursion for transfer systems on certain combinations of bounded posets, we apply these results to determine the full lattice of transfer systems for rank two elementary abelian groups.
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- Award ID(s):
- 2204365
- PAR ID:
- 10634004
- Publisher / Repository:
- Tunisian Mathematical Society
- Date Published:
- Journal Name:
- Tunisian Journal of Mathematics
- Volume:
- 7
- Issue:
- 1
- ISSN:
- 2576-7658
- Page Range / eLocation ID:
- 167-191
- Subject(s) / Keyword(s):
- equivariant homotopy theory transfer systems saturated transfer systems modular lattices
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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