Mod-2 Equivalence of the K-theoretic Euler and Signature Classes

2008/04/06 by James F. Davis, Davis, James F., Pisheng Ding +1
Computer Science · Mathematics · #19K56 #19L99 #57R20 #58J05 #Advanced Algebra and Logic #FOS: Mathematics #Geometric Topology (math.GT) #K-Theory and Homology (math.KT) #Rings, Modules, and Algebras #math.GT #math.KT #msc:19K56 #msc:19L99 #msc:57R20 #msc:58J05 #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.0804.0927

8 pages

arxiv created 2008/04/06 · openalex publication_date 2008/04/06 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This note proves that, as K-theory elements, the symbol classes of the de Rham operator and the signature operator on a closed manifold of even dimension are congruent mod 2. An equivariant generalization is given pertaining to the equivariant Euler characteristic and the multi-signature.

Related

• Euler homology
• Codimension 2 transfer of signatures in L theory
• The Signature of a Manifold
• Pfaffians, the G-Signature Theorem and Galois de Rham discriminants
• Stratified surgery and K-theory invariants of the signature operator