From Mennicke symbols to Euler class groups

Details From Mennicke symbols to Euler class groups From Mennicke symbols to Euler class groups

2000-10-25

arxiv.org/abs/math/0010226v1

Proceedings of the International Colloquium on Algebra, Arithmetic and Geometry. Mumbai 2000, Part II, 341-354

Mathematics

K-Theory and Homology

11 pages, to appear in the Proceedings of the International Colloquium on Algebra, Arithmetic and Geometry. TIFR, Mumbai, Janu

Scientific paper

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.

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