hirzebruch造句

• Friedrich Hirzebruch was, and Yuri Manin is, acting as emeriti.
• There, she was an assistant with Professor Friedrich Hirzebruch.
• The institute was founded in 1980 by Friedrich Hirzebruch.
• This follows from the Atiyah Hirzebruch spectral sequence.
• Physicist typically want to calculate twisted K-theory using the Atiyah Hirzebruch spectral sequence.
• For example, consider the constraint on the Atiyah-Hirzebruch spectral sequence ( AHSS ):
• This is precisely the Atiyah-Hirzebruch spectral sequence construction of twisted K-theory as a set.
• Borel and Hirzebruch showed that the inequality is best possible by finding infinitely many cases where equality holds.
• In the mid-20th century, the Riemann Roch theorem was generalized by Friedrich Hirzebruch to all algebraic varieties.
• Atiyah and Hirzebruch quickly transported Grothendieck's construction to topology and used it to define topological K-theory.
• It is an oriented cobordism invariant, which is expressed in terms of the Pontrjagin numbers by the Hirzebruch signature theorem.
• Massey products of higher order appear when computing twisted K-theory by means of the Atiyah Hirzebruch spectral sequence ( AHSS ).
• In 1956, he applied the same thinking to the Riemann Roch theorem, which had already recently been generalized to any dimension by Hirzebruch.
• With Hirzebruch he extended the Grothendieck Riemann Roch theorem to complex analytic embeddings, they showed that the Hodge conjecture for integral cohomology is false.
• Atiyah's mathematical collaborators include Raoul Bott, Friedrich Hirzebruch and Isadore Singer, and his students include Graeme Segal, Nigel Hitchin and Simon Donaldson.
• One is a Hirzebruch surface given by the blow up of the projective plane at one point, which has 1 ( & minus; 1 )-curves.
• Quillen therefore generalized Lichtenbaum's conjecture, predicting the existence of a spectral sequence like the Atiyah Hirzebruch spectral sequence in topological " K "-theory.
• This is a loop space analogue of the Atiyah-Hirzebruch ?vanishing theorem for group actions and the loop space ?genus, or the Witten genus.
• In fact the index theorem gave a more powerful result, because its proof applied to all compact complex manifolds, while Hirzebruch's proof only worked for projective manifolds.
• Together with Hirzebruch, he laid the foundations for topological K-theory, an important tool in algebraic topology, which, informally speaking, describes ways in which spaces can be twisted.