Spin^{\rm c} -manifolds with Pin(2)-action |
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Authors: | Anand Dessai |
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Institution: | (1) Department of Mathematics, University of Augsburg, D-86135 Augsburg, Germany (e-mail: dessai@mathpool.Uni-Augsburg.DE; http://www.math.Uni-Augsburg.DE/geo/dessai/ homepage.html) , DE |
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Abstract: | We study -manifolds with Pin(2)-action. The main tool is a vanishing theorem for certain indices of twisted -Dirac operators. This theorem is used to show that the Witten genus vanishes on such manifolds provided the first Chern class
and the first Pontrjagin class are torsion. We apply the vanishing theorem to cohomology complex projective spaces and give
partial evidence for a conjecture of Petrie. For example we prove that the total Pontrjagin class of a cohomology with -action has standard form if the first Pontrjagin class has standard form. We also determine the intersection form of certain
4-manifolds with Pin(2)-action.
Received: 26 June 1998 |
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Keywords: | Mathematics Subject Classification (1991):19L47 19J35 55R91 |
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