2025/11/21 by So, Tseleung, Stanley, Donald, Theriault, Stephen +1
#55P99 #55T20 #Algebraic Topology (math.AT) #FOS: Mathematics #Primary 55N10 Secondary 13F55 #Rings and Algebras (math.RA)
paper · doi:10.48550/arxiv.2511.16910
The realization problem asks which algebras can be realized as the cohomology of spaces. We study this problem in the context of the orders in a graded rational exterior algebra on three generators. An order is a subring whose underlying additive group is a lattice. We give conditions for when such an order is realizable, and in particular show that in the simply-connected case any order is realizable if the generators of the exterior algebra are odd.