Vijay Kumar Patodi was a brilliant Indian mathematician who made, during his short life, fundamental contributions to the analytic proof of the index theorem and to the study of differential geometric invariations of manifolds. This volume includes his pathbreaking papers on the McKean-Singer conjecture and the analytic proof of Riemann-Roch-Hirzebruch theorem for Kaehler manifolds. It also contains his celebrated joint papers on the index theorem and the Atiyah-Patodi-Singer invariant.

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