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Rank Constrained Homotopies Of Matrices And The Blackadar-Handelman Conjectures On C*-Algebras, Kaushika De Silva

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Rank constrained homotopies of matrices:

For any n ≥ k ≥ l ∈ N, let S( n,k,l) be the set of all non-negative definite matrices a ∈ Mn(C) with l ≤ rank a ≤ k. We investigate homotopy equivalence of continuous maps from a compact Hausdorff space X into sets of the form S(n,k,l). From [37] it is known that for any n, if 4dim X ≤ k-l where dim X denote the covering dimension of X, then there is exactly one homotopy class of maps from X into S …