2020/07/17 by David Brook, Brook, David
Mathematics · Physics and Astronomy · #19L50 (Primary) 46L80 #55T25 (Secondary) #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT)
paper · pdf · doi:10.48550/arxiv.2007.08964
openalex publication_date 2020/07/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Higher twisted K-theory is an extension of twisted K-theory introduced by Ulrich Pennig which captures all of the homotopy-theoretic twists of topological K-theory in a geometric way. We give an overview of his formulation and key results, and reformulate the definition from a topological perspective. We then investigate ways of producing explicit geometric representatives of the higher twists of K-theory viewed as cohomology classes in special cases using the clutching construction and when the class is decomposable. Atiyah-Hirzebruch and Serre spectral sequences are developed and information on their differentials is obtained, and these along with a Mayer-Vietoris sequence in higher twisted K-theory are applied in order to perform computations for a variety of spaces.