2014/03/19 by Joseph Migler, Migler, Joseph
Computer Science · Mathematics · Physics and Astronomy · #18G35 #47B35 #Computational Physics and Python Applications #FOS: Mathematics #K-Theory and Homology (math.KT) #Operator Algebras (math.OA) #Primary 19C20 #Scientific Research and Discoveries #Secondary 47A13 #math.KT #math.OA #msc:18G35 #msc:19C20 #msc:47A13 #msc:47B35
paper · pdf · doi:10.48550/arxiv.1403.4882
26 pages
arxiv created 2014/03/19 · openalex publication_date 2014/03/19 · arxiv updated 2014/09/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A determinant in algebraic K-theory is associated to any two almost commuting Fredholm operators. On the other hand, one can calculate a homologically defined invariant known as joint torsion. We answer in the affirmative a conjecture of Richard Carey and Joel Pincus, namely that these two invariants agree. In particular, this implies that joint torsion is norm continuous, depends only on the images of the operators modulo trace class, and satisfies the expected Steinberg relations. Moreover, we show that the determinant invariant of two commuting operators can be computed simply as a determinant on a finite dimensional vector space.