3 problems

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Rosenberg's homotopy invariance conjecture for negative K-groups
Let $A$ be a real C-algebra, let $K$ denote nonconnective algebraic $K$ -theory, and let $\mathscr{C}([0,1];A)$ be the ring of continuous functions from $[0,1]$ to $A$ . Rosenberg's…
Conjectureopenalgebraic-k-theory c-star-algebras homotopy-invariancearXiv posted 2 days ago
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Homotopy invariance of $L^2$ torsion
Let $M$ and $N$ be compact odd-dimensional manifolds, and let $f:M\to N$ be a homotopy equivalence. Let $\widehat M$ and $\widehat N$ be their normal $\Gamma$ -covering spaces, and…
Conjectureopencovering-spaces homotopy-invariance l2-torsionarXiv posted 2 days ago
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Oriented-homotopy invariance conjecture for higher string topology operations
Oriented-homotopy invariance conjecture. The operations of the main theorem and the conjectured relative string topology operations are oriented-homotopy invariant.
Conjectureopenhomotopy-invariance string-topologyarXiv posted 2 days ago

Rosenberg's homotopy invariance conjecture for negative K-groups