Topological Structures

Thursday, March 6, 2014 - 3:15pm - 4:05pm
Yasu Hiraoka (Kyushu University)
In this talk, I present a new method to detect robust common topological structures of two geometric objects. The idea is to extend the notion of persistent homology to representations on a commutative triple ladder quiver. (i) I show that representations on the commutative triple ladder quiver are finite type. (ii) The Auslander-Reiten quiver of the commutative triple ladder, which lists up all the possible isomorphism classes of indecomposable persistence modules and irreducible morphisms among them, is explicitly derived.
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