The Topology of the Spectrum for Gelfand Pairs on Lie Groups
Given a Gelfand pair of Lie groups, we identify the spectrum with a suitable subset of and we prove the equivalence between Gelfand topology and euclidean topology.
Gysin Map and Atiyah-Hirzebruch Spectral Sequence
We discuss the relations between the Atiyah-Hirzebruch spectral sequence and the Gysin map for a multiplicative cohomology theory, on spaces having the homotopy type of a finite CW-complex. In particular, let us fix such a multiplicative cohomology theory and let us consider a smooth manifold of dimension and a compact submanifold of dimension , satisfying suitable hypotheses about orientability. We prove that, starting the Atiyah-Hirzebruch spectral sequence with the Poincaré dual of...
Revisiting Pinors and Orientability
We study the relations between pin structures on a non-orientable even-dimensional manifold, with or without boundary, and pin structures on its orientable double cover, requiring the latter to be invariant under sheet-exchange. We show that there is not a simple bijection, but that the natural map induced by pull-back is neither injective nor surjective: we thus find the conditions to recover a full correspondence. We then consider the example of surfaces, with detailed computations for the real...
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