These notes represent the subject of five lectures which were delivered as a minicourse during the VI conference in Krynica, Poland, “Geometry and Topology of Manifolds”, May, 2–8, 2004.
The Evens-Lu-Weinstein representation (Q A, D) for a Lie algebroid A on a manifold M is studied in the transitive case. To consider at the same time non-oriented manifolds as well, this representation is slightly modified to (Q Aor, Dor) by tensoring by orientation flat line bundle, Q Aor=QA⊗or (M) and D or=D⊗∂Aor. It is shown that the induced cohomology pairing is nondegenerate and that the representation (Q Aor, Dor) is the unique (up to isomorphy) line representation for which the top group of...
The contents of the article represents the minicourse which was delivered at the 7th conference "Geometry and Topology of Manifolds. The Mathematical Legacy of Charles Ehresmann", Będlewo (Poland), 8.05.2005 - 15.05.2005. The article includes the description of the so called Hirzebruch formula in different aspects which lead to a basic list of problems related to noncommutative geometry and topology. In conclusion, two new problems are presented: about almost flat bundles and about the Noether decomposition...
Page 1