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- W3046433765 abstract "We introduce an analytic method that uses the global dimension function $operatorname{gldim}$ to produce contractible flows on the space $operatorname{Stab}mathcal{D}$ of stability conditions on a triangulated category $mathcal{D}$. In the case when $mathcal{D}=mathcal{D}(mathbf{S}^lambda)$ is the topological Fukaya category of a graded surface $mathbf{S}^lambda$, we show that $operatorname{gldim}^{-1}(0,y)$ contracts to $operatorname{gldim}^{-1}(0,x)$ for any $1le xle y$, provided $(x,y)$ does not contain `critical' values ${1+w_partial/m_partial mid w_partialge0, partialinpartialmathbf{S}^lambda}$, where the pair $(m_partial,w_partial)$ consists of the number $m_partial$ of marked points and the winding number $w_partial$ associated to a boundary component $partial$ of $mathbf{S}^lambda$. One consequence is that the global dimension of $mathcal{D}(mathbf{S}^lambda)$ must be one of these critical values. Besides, we remove the assumptions in Kikuta-Ouchi-Takahashi's classification result on triangulated categories with global dimension less than 1." @default.
- W3046433765 created "2020-08-07" @default.
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- W3046433765 date "2020-08-01" @default.
- W3046433765 modified "2023-09-27" @default.
- W3046433765 title "Contractible flow of stability conditions via global dimension function" @default.
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- W3046433765 doi "https://doi.org/10.48550/arxiv.2008.00282" @default.
- W3046433765 hasPublicationYear "2020" @default.
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