Generalised homotopy and commutativity principle

• Main Authors: Rao, Ravi A, Sharma, Sampat
• Format: Journal Article
• Language: English
• Published: 08-11-2022
• Subjects: Mathematics - K-Theory and Homology
• DOI: 10.48550/arxiv.2211.04111

In this paper, we study the action of special $n\times n $ linear (resp.
symplectic) matrices which are homotopic to identity on the right invertible
$n\times m$ matrices. We also prove that the commutator subgroup of
$\rm{O}_{2n}(R[X])$ is two stably elementary orthogonal for a local ring $R$
with $\frac{1}{2}\in R$ and $n\geq 3.$