María Constanza Guzmán Martínez. Mapping Spaces of Translation in Twentieth- Century Latin American Print Culture.

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Bott–Thom isomorphism, Hopf bundles and Morse theory

Based on Morse theory for the energy functional on path spaces we develop a deformation theory for mapping spaces of spheres into orthogonal groups. This is used to show that these mapping spaces are weakly homotopy equivalent, in a stable range, to mapping spaces associated to orthogonal Clifford representations. Given an oriented Euclidean bundle $$V \rightarrow X$$ V → X of rank divisible by four over a finite complex X we derive a stable decomposition result for vector bundles over the sphere bundle $$\mathord {{\mathbb {S}}}( \mathord {{\mathbb {R}}}\oplus V)$$ S ( R ⊕ V ) in terms of vector bundles and Clifford module bundles over X. After passing to topological K-theory these results imply classical Bott–Thom isomorphism theorems.