notesum.ai

Published at November 28

Decomposing zero-dimensional persistent homology over rooted tree quivers

math.RT

cs.CG

math.AT

Released Date: November 28, 2024

Authors: Riju Bindua, Thomas Brüstle, Luis Scoccola

Arxiv: http://arxiv.org/pdf/2411.19319v1

Refer to caption

Rooted tree poset (a type of poset)	Sec. 2.5
Rooted tree quiver (a type of quiver)	Sec. 2.1
Rooted tree quiver over a rooted tree quiver $Q$ (a type of quiver morphism $T\xrightarrow{\;\;\;}Q$ )	Sec. 2.4
Linearized rooted tree quiver over a rooted tree quiver $Q$ (a type of representation of $Q$ )	Def. 2.17
Rooted tree module over a quiver $Q$ (a type of representation of $Q$ )	Def. 2.23
Reduced rooted tree quiver over a rooted tree quiver $Q$ (a type of quiver morphism $T\xrightarrow{\;\;\;}Q$ )	Def. 2.15
Reduced rooted tree module over a rooted tree quiver $Q$ (a type of representation of $Q$ )	Def. 2.25
Order $\leq_{Q}$ (an order on vertices of a tree quiver $Q$ )	Def. 2.1
Preorder $\preceq_{Q}$ (a preorder on rooted tree quivers over a rooted tree quiver $Q$ )	Def. 2.14