An Introduction to Noncommutative Spaces and their Geometry
by Giovanni Landi
Publisher: arXiv 1997
Number of pages: 186
These lectures notes are an introduction for physicists to several ideas and applications of noncommutative geometry. The necessary mathematical tools are presented in a way which we feel should be accessible to physicists. We illustrate applications to Yang-Mills, fermionic and gravity models, notably we describe the spectral action recently introduced by Chamseddine and Connes. We also present an introduction to recent work on noncommutative lattices.
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by Alain Connes, Matilde Marcolli - American Mathematical Society
The unifying theme of this book is the interplay among noncommutative geometry, physics, and number theory. The two main objects of investigation are spaces where both the noncommutative and the motivic aspects come to play a role.
by Vincent Bouchard - arXiv
These are introductory lecture notes on complex geometry, Calabi-Yau manifolds and toric geometry. We first define basic concepts of complex and Kahler geometry. We then proceed with an analysis of various definitions of Calabi-Yau manifolds.
by C. Nash - arXiv
In this essay we wish to embark on the telling of a story which, almost certainly, stands only at its beginning. We shall discuss the links and the interaction between one very old subject, physics, and a much newer one, topology.
by Gabriel Lugo - University of North Carolina at Wilmington
These notes were developed as a supplement to a course on Differential Geometry at the advanced undergraduate level, which the author has taught. This texts has an early introduction to differential forms and their applications to Physics.