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Smooth Structures on Complex Projective Spaces

Dr. Ramesh Kasilingam Indian Statistical Institute, Bangalore
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Dr. Ramesh Kasilingam Indian Statistical Institute, Bangalore
When Apr 24, 2018
from 04:00 PM to 05:00 PM
Where LH 006
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Abstract: A smooth manifold homeomorphic to the standard sphere m-sphere is known as a smooth homotopy m-sphere. The existence of smooth homotopy m-spheres was studied in the amazing work of Kervaire and Milnor. The set of diffeomorphism classes of smooth homotopy m-spheres m (m > 4) forms a group under the operation of connected sum and is related to computations in stable homotopy theory. Using these computations, we determine the number of smooth structures on the n-dimensional complex projective space for n < 9 (up to  > isotopy, more precisely, concordance).

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