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In mathematics, the Bott periodicity theorem describes a periodicity in the homotopy groups of classical groups, discovered by Raoul Bott (1957, 1959), which proved to be of foundational significance for much further research, in particular in K-theory of stable complex vector bundles, as well as the stable homotopy groups of spheres.
Raoul Bott (September 24, 1923 – December 20, 2005) [1] was a Hungarian-American mathematician known for numerous foundational contributions to geometry in its broad sense. He is best known for his Bott periodicity theorem , the Morse–Bott functions which he used in this context, and the Borel–Bott–Weil theorem .
Raoul Bott used Morse–Bott theory in his original proof of the Bott periodicity theorem. Round functions are examples of Morse–Bott functions, where the critical sets are (disjoint unions of) circles. Morse homology can also be formulated for Morse–Bott functions; the differential in Morse–Bott homology is computed by a spectral ...
The abstract theory of Clifford modules was founded by a paper of M. F. Atiyah, R. Bott and Arnold S. Shapiro. A fundamental result on Clifford modules is that the Morita equivalence class of a Clifford algebra (the equivalence class of the category of Clifford modules over it) depends only on the signature p − q (mod 8).
Furthermore, the table assumes the limit of an infinite number of bands, i.e. involves Hamiltonians for . The table also is periodic in the sense that the group of invariants in dimensions is the same as the group of invariants in + dimensions. In the case of no ant-iunitary symmetries, the invariant groups are periodic in dimension by 2.
Listing price on eBay: $2,500 There were countless Japanese-made, cartoon-like ceramic figurines made during the 1950s, and some of the most valuable (and collectible) are vintage salt and pepper ...
The NFL playoff schedule is about to be set, with the wild-card dates and times for every matchup to be revealed during Week 18.
The oldest known tablet inscribed with the Ten Commandments from the Old Testament sold on Wednesday for $5.04 million, more than double its high estimate.. The stone, which dates back around ...