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Macquarie University  Department of Mathematics

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Workshop on Categorical Methods in Algebra, Geometry and Mathematical Physics

Satellite to the StreetFest conference in honour of Ross Street's sixtieth birthday

July 18-21 2005, Australian National University, Canberra

Mon, 18 July:  16:40 - 17:20

Interpolation categories for homology theories
Biedermann, Georg (University of Western Ontario)

For a homological functor from a triangulated category to an abelian category satisfying some technical assumptions we construct a tower of interpolation categories.
These are categories over which the functor factorizes and which capture more and more information according to the injective dimension of the images of the functor. The categories are obtained by proving the existence of truncated versions of resolution or $E_2$-model structures. Examples of functors fitting in our framework are given by every generalized homology theory represented by a ring spectrum satisfying the Adams--Atiyah condition. The constructions are closely related to the modified Adams spectral sequence and give a very conceptual approach to the associated moduli problem and obstruction theory.
As application we establish an isomorphism between certain $E(n)$-local Picard groups and some Ext-groups.

Typeset PDF of this abstract.