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- W2025131206 abstract "We establish a link between rational homotopy theory and the problem which vector bundles admit a complete Riemannian metric of nonnegative sectional curvature. As an application, we show for a large class of simply-connected nonnegatively curved manifolds that, if <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper C> <mml:semantics> <mml:mi>C</mml:mi> <mml:annotation encoding=application/x-tex>C</mml:annotation> </mml:semantics> </mml:math> </inline-formula> lies in the class and <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper T> <mml:semantics> <mml:mi>T</mml:mi> <mml:annotation encoding=application/x-tex>T</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is a torus of positive dimension, then “most” vector bundles over <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper C times upper T> <mml:semantics> <mml:mrow> <mml:mi>C</mml:mi> <mml:mo>×<!-- × --></mml:mo> <mml:mi>T</mml:mi> </mml:mrow> <mml:annotation encoding=application/x-tex>Ctimes T</mml:annotation> </mml:semantics> </mml:math> </inline-formula> admit no complete nonnegatively curved metrics." @default.
- W2025131206 created "2016-06-24" @default.
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- W2025131206 date "2002-12-03" @default.
- W2025131206 modified "2023-10-18" @default.
- W2025131206 title "Obstructions to nonnegative curvature and rational homotopy theory" @default.
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