Year: 2026
Type: preprint
Abstract: This paper investigates the Mayer-Vietoris sequence for the Milnor square. While such sequences often involve elusive intermediate terms, we provide an explicit characterization of the key group $X$ in a new, more general variant of the sequence. By identifying $X$ as a categorical pullback, we provide a full, constructive proof of the modified Mayer-Vietoris sequence. Furthermore, we show that $X$ fits into a structural exact sequence involving the relative $K$-groups $K_{*}(A, B, I)$. Finally, we provide a homotopy-theoretic description of $X$ as the homotopy group of a suitable fiber, clarifying its structure, kernel , and image.
Source: arXiv (Cornell University)
Author: Zhang, Yakun
Institution: Nanjing Audit University
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7138138573
Cites:
Cited by:
Related to: