# One-relator groups and algebras related to polyhedral products

15 Aug 2020 Grbić Jelena Ilyasova Marina Panov Taras Simmons George

We link distinct concepts of geometric group theory and homotopy theory through underlying combinatorics. For a flag simplicial complex $K$, we specify a necessary and sufficient combinatorial condition for the commutator subgroup $RC_K'$ of a right-angled Coxeter group, viewed as the fundamental group of the real moment-angle complex $\mathcal{R}_K$, to be a one-relator group; and for the Pontryagin algebra $H_*(\Omega \mathcal{Z}_K)$ of the moment-angle complex to be a one-relator algebra... (read more)

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# Categories

• ALGEBRAIC TOPOLOGY
• COMBINATORICS
• GROUP THEORY