Corresponding module and ordered groupoid sequences

Bernard Bainson (Heriot Watt)

Wednesday 26th October, 2016 16:00-17:00 Maths 522


The theory of ordered groupoids , a legacy of C. Ehresmann arose as an abstract theory to that of pseudogroups of transformations. Ordered groupoids have since played crucial roles in modern discussions of geometry and has provided remarkable extensions of concepts in group theory. In this light,  I will describe the construction derivation module of ordered functors generalising the construction for groups by Crowell in 1961. I will show that for some sequences of ordered functors of ordered groupoids analogous to that of Crowell, there are corresponding sequence of module maps.  The most familiar application is the construction of the five-term exact sequence of low dimensional (co)homology groups.

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