Geodesic
Knörrer periodicity and Bott periodicity
Documenta mathematica, Tome 21 (2016), pp. 1459-1501.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

The goal of this article is to explain a precise sense in which Knörrer periodicity in commutative algebra and Bott periodicity in topological $K$-theory are compatible phenomena. Along the way, we prove an 8-periodic version of Knörrer periodicity for real isolated hypersurface singularities, and we construct a homomorphism from the Grothendieck group of the homotopy category of matrix factorizations of a complex (real) polynomial $f$ into the topological $K$-theory of its Milnor fiber (positive or negative Milnor fiber).
Classification : 13D15, 18D20, 18E30, 32S55, 55N15
Keywords: Atiyah-Bott-Shapiro construction, Bott periodicity, Knörrer periodicity, matrix factorizations, Milnor fibration 
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     author = {Brown, Michael K.},
     title = {Kn\"orrer periodicity and {Bott} periodicity},
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     volume = {21},
     year = {2016},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DOCMA_2016__21__a6/}
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Brown, Michael K. Knörrer periodicity and Bott periodicity. Documenta mathematica, Tome 21 (2016), pp. 1459-1501. http://geodesic.mathdoc.fr/item/DOCMA_2016__21__a6/