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Homology and modular classes of Lie algebroids

Janusz Grabowski, Giuseppe Marmo, Peter W. Michor (2006)

Annales de l’institut Fourier

For a Lie algebroid, divergences chosen in a classical way lead to a uniquely defined homology theory. They define also, in a natural way, modular classes of certain Lie algebroid morphisms. This approach, applied for the anchor map, recovers the concept of modular class due to S. Evens, J.-H. Lu, and A. Weinstein.

Homology of gaussian groups

Patrick Dehornoy, Yves Lafont (2003)

Annales de l’institut Fourier

We describe new combinatorial methods for constructing explicit free resolutions of ℤ by ℤ G -modules when G is a group of fractions of a monoid where enough lest common multiples exist (“locally Gaussian monoid”), and therefore, for computing the homology of G . Our constructions apply in particular to all Artin-Tits groups of finite Coexter type. Technically, the proofs rely on the properties of least common multiples in a monoid.

Homology theory in the alternative set theory I. Algebraic preliminaries

Jaroslav Guričan (1991)

Commentationes Mathematicae Universitatis Carolinae

The notion of free group is defined, a relatively wide collection of groups which enable infinite set summation (called commutative π -group), is introduced. Commutative π -groups are studied from the set-theoretical point of view and from the point of view of free groups. Commutativity of the operator which is a special kind of inverse limit and factorization, is proved. Tensor product is defined, commutativity of direct product (also a free group construction and tensor product) with the special...

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