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A functional S-dual in a strong shape category

Friedrich Bauer (1997)

Fundamenta Mathematicae

In the S-category P (with compact-open strong shape mappings, cf. §1, instead of continuous mappings, and arbitrary finite-dimensional separable metrizable spaces instead of finite polyhedra) there exists according to [1], [2] an S-duality. The S-dual D X , X = ( X , n ) P , turns out to be of the same weak homotopy type as an appropriately defined functional dual ( S 0 ) X ¯ (Corollary 4.9). Sometimes the functional object X Y ¯ is of the same weak homotopy type as the “real” function space X Y (§5).

A geometric description of differential cohomology

Ulrich Bunke, Matthias Kreck, Thomas Schick (2010)

Annales mathématiques Blaise Pascal

In this paper we give a geometric cobordism description of differential integral cohomology. The main motivation to consider this model (for other models see [5, 6, 7, 8]) is that it allows for simple descriptions of both the cup product and the integration. In particular it is very easy to verify the compatibilty of these structures. We proceed in a similar way in the case of differential cobordism as constructed in [4]. There the starting point was Quillen’s cobordism description of singular cobordism...

Brown–Peterson cohomology and Morava K-theory of DI(4) and its classifying space

Marta Santos (1999)

Fundamenta Mathematicae

DI(4) is the only known example of an exotic 2-compact group, and is conjectured to be the only one. In this work, we study generalized cohomology theories for DI(4) and its classifying space. Specifically, we compute the Morava K-theories, and the P(n)-cohomology of DI(4). We use the non-commutativity of the spectrum P(n) at p=2 to prove the non-homotopy nilpotency of DI(4). Concerning the classifying space, we prove that the BP-cohomology and the Morava K-theories of BDI(4) are all concentrated...

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