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Some differential complexes within and beyond parabolic geometry

Publication ,  Journal Article
Bryant, RL; Eastwood, MG; Gover, AR; Neusser, K
Published in: Advanced Studies in Pure Mathematics
November 22, 2019

For smooth manifolds equipped with various geometric structures, we construct complexes that replace the de Rham complex in providing an alternative fine resolution of the sheaf of locally constant functions. In case that the geometric structure is that of a parabolic geometry, our complexes coincide with the Bernstein-Gelfand-Gelfand complex associated with the trivial representation. However, at least in the cases we discuss, our constructions are relatively simple and avoid most of the machinery of parabolic geometry. Moreover, our method extends to certain geometries beyond the parabolic realm.

Duke Scholars

Published In

Advanced Studies in Pure Mathematics

Publication Date

November 22, 2019

Volume

82

Issue

Differential Geometry and Tanaka Theory

Start / End Page

13 / 40

Publisher

Mathematical Society of Japan
 

Citation

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Bryant, R. L., Eastwood, M. G., Gover, A. R., & Neusser, K. (2019). Some differential complexes within and beyond parabolic geometry. Advanced Studies in Pure Mathematics, 82(Differential Geometry and Tanaka Theory), 13–40.
Bryant, R. L., M. G. Eastwood, A. R. Gover, and K. Neusser. “Some differential complexes within and beyond parabolic geometry.” Advanced Studies in Pure Mathematics 82, no. Differential Geometry and Tanaka Theory (November 22, 2019): 13–40.
Bryant RL, Eastwood MG, Gover AR, Neusser K. Some differential complexes within and beyond parabolic geometry. Advanced Studies in Pure Mathematics. 2019 Nov 22;82(Differential Geometry and Tanaka Theory):13–40.
Bryant, R. L., et al. “Some differential complexes within and beyond parabolic geometry.” Advanced Studies in Pure Mathematics, vol. 82, no. Differential Geometry and Tanaka Theory, Mathematical Society of Japan, Nov. 2019, pp. 13–40.
Bryant RL, Eastwood MG, Gover AR, Neusser K. Some differential complexes within and beyond parabolic geometry. Advanced Studies in Pure Mathematics. Mathematical Society of Japan; 2019 Nov 22;82(Differential Geometry and Tanaka Theory):13–40.

Published In

Advanced Studies in Pure Mathematics

Publication Date

November 22, 2019

Volume

82

Issue

Differential Geometry and Tanaka Theory

Start / End Page

13 / 40

Publisher

Mathematical Society of Japan