nLab Peter Michor

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Selected writings

On manifold structure of mapping spaces:

via Fréchet manifolds:

• Peter Michor: Manifolds of Differentiable Mappings, Shiva Publishing (1980) [pdf, pdf]

via Frölicher spaces:

• Peter W. Michor: Manifolds of mappings and shapes, in: Lizhen Ji, Frans Oort, Shing-Tung Yau (eds.): The legacy of Bernhard Riemann after one hundred and fifty years, ALM 35, International Press Boston (2016) 459–486 [arXiv:1505.02359 math.DG]

• Peter W. Michor: Manifolds of mappings for continuum mechanics, in: Reuven Segev, Marcelo Epstein (eds).: Geometric Continuum Mechanics, Advances in Continuum Mechanics 42, Birkhäuser (2020) 3–75 [doi:10.1007/978-3-030-42683-5_1, arXiv:1909.00445 math.DG]

On $C^\infty$ algebras and functional analysis:

• G. Kainz, Andreas Kriegl, Peter Michor: $C^\infty$-algebras from the functional analytic view point, Journal of Pure and Applied Algebra 46 1 (1987) 89-107 [doi:10.1016/0022-4049(87)90045-4 pdf]

Characterizing the Schouten-Nijenhuis bracket as a natural operation:

• Peter W. Michor, Remarks on the Schouten-Nijenhuis bracket, In: J. Bureš, V. Souček (eds.): Proceedings of the Winter School “Geometry and Physics” Circolo Matematico di Palermo, Palermo (1987) 207-215 [dml:701423, pdf, pdf]

On differential geometry with focus on natural bundles:

• Ivan Kolář, Peter Michor, Jan Slovák, Natural operations in differential geometry, Springer (1993) [book webpage, doi:10.1007/978-3-662-02950-3

  pdf]

On $C^\infty$-rings:

• Peter Michor, Jiří Vanžura: Characterizing algebras of $C^\infty$-functions on manifolds, Comment. Math. Univ. Carolin. 37 3 (1996) 519–521

  [arXiv:math/9404228, eudml:247941, pdf]

On differential geometry in terms of Frölicher spaces and diffeological spaces, in particular also on infinite-dimensional manifolds:

• Andreas Kriegl, Peter Michor: The Convenient Setting of Global Analysis: Mathematical Surveys and Monographs 53, American Mathematical Society (1997) [ISBN: 978-0-8218-0780-4, ams:surv-53, pdf]

A textbook on differential geometry, including an account of Schouten–Nijenhuis bracket, Frölicher–Nijenhuis bracket, and Nijenhuis–Richardson bracket:

• Peter W. Michor, Topics in Differential Geometry, Graduate Studies in Mathematics 93 (2008). PDF.

On Moser's theorem generalized to manifolds with corners:

• Martins Bruveris, Peter W. Michor, Adam Parusinski, Armin Rainer: Moser’s theorem on manifolds with corners, Proc. Amer. Math. Soc. 146 11 (2018) 4889-4897 [doi:10.1090/proc/14130, arXiv:1604.07787]

Related entries

• generalized smooth space

• C∞-ring

• Milnor's exercise

• module over a $C^\infty$-ring

category: people