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非可換幾何学に関する解説書もいろいろ出ている。 年代順に挙げると以下の通り。
- Connes の解説書 [Con90] (フランス語)
- Manin の [Man91]
- Connes の解説書 [Con94] (英語)
- Landi の [Lan97] (物理の人向け) と [Lan07] (gauge theory が目的)
- Gracia-Bondia と Varilly と Figueroa の本 [GVF01]
- Connes の [Con00]
- Varilly の [Var]
- Khalkhali の解説 [Kha]
- Marcolli の [Mar05]
- Ginzburg の [Gin]
- Connes と Marcolli の [CM08]
- Khalkhali の [Kha08]
Ginzburg のものは, Atiyah algebra や Morita同値などの代数的な基礎から書いてあって, 読みやすい。
解説書とは言えないが, Skoda の [Ško06] は, 非可換 (代数) 幾何学の様々なアイデアを概観するのによいと思う。
Euclid 空間の幾何学を非可換化しようという試みについては, Banica の [Ban] がある。
References
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[Ban]
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Teo Banica. Affine noncommutative geometry. arXiv: 2012.10973.
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[CM08]
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Alain Connes and Matilde Marcolli. “A walk in the noncommutative
garden”. In: An invitation to noncommutative geometry. World Sci.
Publ., Hackensack, NJ, 2008, pp. 1–128. arXiv: math/0601054. url:
http://dx.doi.org/10.1142/9789812814333_0001.
-
[Con00]
-
Alain Connes. “Noncommutative geometry—year 2000”. In: Geom.
Funct. Anal. Special Volume, Part II (2000). GAFA 2000 (Tel Aviv,
1999), pp. 481–559. arXiv: math.QA/0011193.
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[Con90]
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Alain Connes. Géométrie non commutative. Paris: InterEditions,
1990, p. 240. isbn: 2-7296-0284-4.
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[Con94]
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Alain Connes. Noncommutative geometry. San Diego, CA: Academic
Press Inc., 1994, pp. xiv+661. isbn: 0-12-185860-X.
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[Gin]
-
Victor Ginzburg. Lectures on Noncommutative Geometry. arXiv:
math/0506603.
-
[GVF01]
-
José M. Gracia-Bondía, Joseph C. Várilly, and Héctor Figueroa.
Elements of noncommutative geometry. Birkhäuser Advanced Texts:
Basler Lehrbücher. [Birkhäuser Advanced Texts: Basel Textbooks].
Birkhäuser
Boston, Inc., Boston, MA, 2001, pp. xviii+685. isbn: 0-8176-4124-6.
url: http://dx.doi.org/10.1007/978-1-4612-0005-5.
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[Kha]
-
Masoud Khalkhali. Very Basic Noncommutative Geometry. arXiv:
math/0408416.
-
[Kha08]
-
Masoud Khalkhali. “Lectures on noncommutative geometry”. In:
An invitation to noncommutative geometry. World Sci. Publ.,
Hackensack, NJ, 2008, pp. 169–273. arXiv: math/0702140. url:
http://dx.doi.org/10.1142/9789812814333_0003.
-
[Lan07]
-
Giovanni Landi. “Examples of noncommutative instantons”. In:
Geometric and topological methods for quantum field theory.
Vol. 434. Contemp. Math. Providence, RI: Amer. Math. Soc., 2007,
pp. 39–72. arXiv: math/0603426.
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[Lan97]
-
Giovanni Landi. An introduction to noncommutative spaces and
their geometries. Vol. 51. Lecture Notes in Physics. New Series
m: Monographs. Berlin: Springer-Verlag, 1997, pp. xii+200. isbn:
3-540-63509-2.
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[Man91]
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Yuri I. Manin. Topics in noncommutative geometry. M. B.
Porter Lectures. Princeton, NJ: Princeton University Press, 1991,
pp. viii+164. isbn: 0-691-08588-9.
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[Mar05]
-
Matilde Marcolli. Arithmetic noncommutative geometry. Vol. 36.
University Lecture Series. With a foreword by Yuri Manin. American
Mathematical Society, Providence, RI, 2005, pp. xii+136. isbn:
0-8218-3833-4. url: http://dx.doi.org/10.1090/ulect/036.
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[Ško06]
-
Zoran Škoda. “Noncommutative localization in noncommutative
geometry”. In: Non-commutative localization in algebra and topology.
Vol. 330. London Math. Soc. Lecture Note Ser. Cambridge:
Cambridge Univ. Press, 2006, pp. 220–313. arXiv: math/0403276.
url: http://dx.doi.org/10.1017/CBO9780511526381.015.
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[Var]
-
Joseph C. Varilly. An Introduction to Noncommutative Geometry.
arXiv: physics/9709045.
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