dorsal/arxiv
View SchemaOn quantum topology, hypergraphs and flag vectors
| Authors | Jonathan Fine |
|---|---|
| Categories | |
| ArXiv ID | q-alg/9708001 |
| URL | https://arxiv.org/abs/q-alg/9708001 |
Abstract
Each rule $f$ that assigns a vector $f(G)$ to an $(n+1)$-graph $G$ determines a class (or property) of $n$-manifold invariants. An invariant $v=v(M)$ is in this class if, for any triangulated manifold $|G|=M$, one has that $v(M)$ is a linear function of $f(G)$. This paper defines a flag vector $f(G)$ for $i$-graphs, whose associated invariants might be quantum, and which is of interest in its own right. The definition (via the concept of shelling, and a `disjoint pair of optional cells' rule for the link) seems to apply to any finite combinatorial object, and so to any compact topological object that can be triangulated. It also applies to finite groups.
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"abstract": "Each rule $f$ that assigns a vector $f(G)$ to an $(n+1)$-graph $G$ determines\na class (or property) of $n$-manifold invariants. An invariant $v=v(M)$ is in\nthis class if, for any triangulated manifold $|G|=M$, one has that $v(M)$ is a\nlinear function of $f(G)$. This paper defines a flag vector $f(G)$ for\n$i$-graphs, whose associated invariants might be quantum, and which is of\ninterest in its own right. The definition (via the concept of shelling, and a\n`disjoint pair of optional cells\u0027 rule for the link) seems to apply to any\nfinite combinatorial object, and so to any compact topological object that can\nbe triangulated. It also applies to finite groups.",
"arxiv_id": "q-alg/9708001",
"authors": [
"Jonathan Fine"
],
"categories": [
"q-alg",
"math.QA"
],
"title": "On quantum topology, hypergraphs and flag vectors",
"url": "https://arxiv.org/abs/q-alg/9708001"
},
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