Browsing by Author "Gomi, Kiyonori"
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- ItemChiral vector bundles(2018) De Nittis, Giuseppe; Gomi, Kiyonori
- ItemDifferential geometric invariants for time-reversal symmetric Bloch bundles II: The low-dimensional "quaternionic" case(2023) De Nittis, Giuseppe; Gomi, KiyonoriThis paper is devoted to the construction of differential geometric invariants for the classification of "quaternionic" vector bundles. Provided that the base space is a smooth manifold of dimension two or three endowed with an involution that leaves fixed only a finite number of points, it is possible to prove that the Wess-Zumino term and the Chern-Simons invariant yield topological invariants able to distinguish between inequivalent realizations of "quaternionic" structures. This is a nontrivial generalization of results previously known only in the case of tori with time-reversal involution.
- ItemHilbert Grassmannians as classifying spaces(2025) De Nittis, Giuseppe; Gomi, Kiyonori; González Rendel, SantiagoIn this short work we prove that the Hilbert Grassmannians endowed with the weak topology are models for the classifying spaces of the unitary groups. As application of this result one can use Hilbert Grassmannians for the presentation of the $K$-theory of topological spaces by computing equivalences classes of homotopy equivalent maps.
- ItemThe cohomological nature of the Fu-Kane-Mele invariant(2018) De Nittis, Giuseppe; Gomi, Kiyonori