3rd installment of Front Range Algebraic Geometry (FRAG) day happening at CSU in Weber 201 1:00-5:00 https://sites.google.com/colorado.edu/front-range-ag/home
FRAG Day
Thu, Oct. 30 2:30pm (MATH 3…
Functional Analysis
Maggie Reardon (CU Boulder)
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Matui’s HK-conjecture proposes a connection between the homology of a nice enough étale groupoid and the -theory of the associated reduced -algebra. The HK-conjecture is not true in general and there are a number of counterexamples. The related AH-conjecture predicts an exact sequence involving the zeroth and first homology groups together with the abelianization of the topological full group. Unlike the HK-conjecture, no counterexamples are known for the AH-conjecture, though it remains unproven. Both conjectures are verified for a number of natural classes of groupoids, including AF groupoids.
Putnam introduced a new class of groupoids in the paper titled “Some classifiable groupoid -algebras with prescribed -theory”. These new groupoids are related to AF groupoids and this prompts a natural question: does this new class of groupoids satisfy the HK- and AH-conjectures?
The HK- and AH-conjectures for certain groupoids constructed by Putnam
FRAG Day