From Mennicke symbols to Euler class groups
摘要
Bhatwadekar and Raja Sridharan have constructed a homomorphism of abelian groups from an orbit set Um(n,A)/E(n,A) of unimodular rows to an Euler class group. We suggest that this is the last map in a longer exact sequence of abelian groups. The hypothetical group G that precedes Um(n,A)/E(n,A) in the sequence is an orbit set of unimodular two by n matrices over the ring A. If n is at least four we describe a partially defined operation on two by n matrices. We conjecture that this operation describes a group structure on G if A has Krull dimension at most 2n-6. We prove that G is mapped onto a subgroup of Um(n,A)/E(n,A) if A has Krull dimension at most 2n-5.
引用
@article{arxiv.math/0010226,
title = {From Mennicke symbols to Euler class groups},
author = {Wilberd van der Kallen},
journal= {arXiv preprint arXiv:math/0010226},
year = {2007}
}
备注
11 pages, to appear in the Proceedings of the International Colloquium on Algebra, Arithmetic and Geometry. TIFR, Mumbai, January 4-12, 2000