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Grassmannian and elliptic operators. (English) Zbl 0923.58053

McCleary, John (ed.), Higher homotopy structures in topology and mathematical physics. Proceedings of an international conference, June 13–15, 1996, Poughkeepsie, NY, USA, to honor the 60th birthday of Jim Stasheff. Providence, RI: American Mathematical Society. Contemp. Math. 227, 79-88 (1999).
The main goal of this paper is to formulate a multi-dimensional analogue of the Krichever construction in terms of the Dirac operator. The arguments used in the proof make possible to replace the multi-dimensional Dirac operator by an arbitrary elliptic differential operator. There are used standard techniques from the theory of pseudodifferential operators. After deducing the main result under the additional assumption that the Agmon-Seeley condition is satisfied, the author shows that this hypothesis can be removed.
For the entire collection see [Zbl 0904.00041].

MSC:

58J32 Boundary value problems on manifolds
35S99 Pseudodifferential operators and other generalizations of partial differential operators
81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory