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Topology of tensor ranks. (English) Zbl 1439.15001

The authors study some topological (in Euclidean and Zariski topology) properties of tensor ranks. Among these properties are: path-connectedness, fundamental groups and higher homotopy groups.
This is an extensive investigation and the authors summarize their results in a quite exhaustive table for tensor ranks over \(\mathbb{C}\) and \(\mathbb{R}\).

MSC:

15A03 Vector spaces, linear dependence, rank, lineability
15A69 Multilinear algebra, tensor calculus
54D05 Connected and locally connected spaces (general aspects)
55Q05 Homotopy groups, general; sets of homotopy classes
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