Cellular sheaves of lattices and the Tarski Laplacian
Cellular sheaves of lattices and the Tarski Laplacian
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DOI：
10.4310/hha.2022.v24.n1.a16
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发表时间：
2020-07
期刊：
影响因子：
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通讯作者：
R. Ghrist;Hans Riess
中科院分区：
文献类型：
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作者：
R. Ghrist;Hans Riess
本文提出了一个离散霍奇理论的细胞层采取的一类格和伽罗瓦连接的价值。关键的发展是塔斯基拉普拉斯算子，上链复形上的自同态，其不动点产生的上同调与零度的整体截面函子一致。这在网络上的共识和分布式优化问题中有直接的应用，并有更广泛的潜在应用。
This paper initiates a discrete Hodge theory for cellular sheaves taking values in a category of lattices and Galois connections. The key development is the Tarski Laplacian, an endomorphism on the cochain complex whose fixed points yield a cohomology that agrees with the global section functor in degree zero. This has immediate applications in consensus and distributed optimization problems over networks and broader potential applications.