A spectral sequence for pseudogroups on

Author:
Solomon M. Jekel

Journal:
Trans. Amer. Math. Soc. **333** (1992), 741-749

MSC:
Primary 58H10; Secondary 57R32

DOI:
https://doi.org/10.1090/S0002-9947-1992-1066445-4

MathSciNet review:
1066445

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Abstract: Consider a pseudogroup of local homeomorphisms of satisfying the following property: given points and in , there is an element of , with domain an interval containing , taking each to . The pseudogroup of local homeomorphisms, , is of this type as is the pseudogroup of local real-analytic homeomorphisms. Let be the topological groupoid of germs of elements of . We construct a spectral sequence which involves the homology of a sequence of discrete groups . Consider the set ,; define if and agree on a neighborhood of . The equivalence classes under composition form the group . *Theorem*: There is a spectral sequence with which converges to . Our spectral sequence can be considered to be a version which covers the realanalytic case of some well-known theorems of J. Mather and G. Segal. The article includes some observations about how the spectral sequence applies to . Further applications will appear separately.

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DOI:
https://doi.org/10.1090/S0002-9947-1992-1066445-4

Article copyright:
© Copyright 1992
American Mathematical Society