On $\tau$-tilting graphs for quasi-silted algebras

Mathematics > Representation Theory [Submitted on 10 Jan 2024 (v1), last revised 18 Jun 2026 (this version, v4)] Title:On $τ$-tilting graphs for quasi-silted algebras View PDF HTML (experimental)Abstract:We prove that the $\tau$-tilting graph of any quasi-silted algebra is connected and has the reachable-in-face property. Our approach utilizes $\tau$-reduction and wall and chamber structures. In particular, we observe a sufficient condition on the wall and chamber structure under which the connectivity of $\tau$-tilting graphs is preserved under taking quotients of algebras. As an immediate consequence, the connectivity of $\tau$-tilting graphs is also established for several new classes of algebras. Submission history From: Shengfei Geng [view email][v1] Wed, 10 Jan 2024 13:44:35 UTC (16 KB) [v2] Thu, 11 Jan 2024 03:09:36 UTC (16 KB) [v3] Thu, 26 Jun 2025 14:50:43 UTC (21 KB) [v4] Thu, 18 Jun 2026 12:07:24 UTC (19 KB) References & Citations Loading... Bibliographic and Citation Tools Bibliographic Explorer (What is the Explorer?) Connected Papers (What is Connected Papers?) Litmaps (What is Litmaps?) scite Smart Citations (What are Smart Citations?) Code, Data and Media Associated with this Article alphaXiv (What is alphaXiv?) CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub (What is DagsHub?) Gotit.pub (What is GotitPub?) Hugging Face (What is Huggingface?) ScienceCast (What is ScienceCast?) Demos Recommenders and Search Tools Influence Flower (What are Influence Flowers?) CORE Recommender (What is CORE?) arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.