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  Far East Journal of Mathematical Sciences (FJMS)  
 ISSN: 0972-0871
 
 
 

     Far East Journal of Mathematical Sciences (FJMS)
    Volume 28, Issue 2, Pages 273 - 290 (February 2008)


ANOTHER COBOUNDARY OPERATOR FOR DIFFERENTIAL FORMS WITH VALUES IN THE LIE ALGEBRA OF A GROUP  A CHAPTER IN SYNTHETIC DIFFERENTIAL GEOMETRY OF GROUPOIDS

Hirokazu Nishimura (Japan)

Received January 5, 2007

References:



[1] L. Breen and W. Messing, Combinatorial differential forms, Adv. Math. 164 (2001), 203-282.

[2] L. Breen and W. Messing, Differential geometry of gerbes, Adv. Math. 198 (2005), 732-846.

[3] A. Kock, Synthetic Differential Geometry, London Mathematical Society Lecture Note Series, 51, Cambridge University Press, Cambridge, 1981.

[4] A. Kock, Differential forms with values in groups (preliminary report), Cahiers Top. Geom. Diff. 22 (1981), 141-148.

[5] A. Kock, Differential forms with values in groups, Bull. Austral. Math. Soc. 25 (1982), 357-386.

[6] A. Kock, Combinatorics of curvature, and the Bianchi identity, Theory and Applications of Categories 2 (1996), 69-89.

[7] R. Lavendhomme, Basic Concepts of Synthetic Differential Geometry, Kluwer, Dordrecht, 1996.

[8] K. C. H. Mackenzie, General Theory of Lie Groupoids and Lie Algebroids, London Mathematical Society Lecture Note Series, 213, Cambridge University Press, Cambridge, 2005.

[9] I. Moerdijk and G. E. Reyes, Models for Smooth Infinitesimal Analysis, Springer-Verlag, New York, 1991.

[10] H. Nishimura, Another curvature in synthetic differential geometry, Bull. Belg. Math. Soc. Simon Stevin 7 (2000), 161-171.

[11] H. Nishimura, The Lie algebra of the group of bisections, Far East J. Math. Sci. (FJMS) 24 (2007), 329-342.

[12] R. W. Sharpe, Differential Geometry: Cartan’s Generalization of Klein’s Erlangen Program, Graduate Texts in Mathematics, 166, Springer-Verlag, New York, 1997.

Keywords and phrases: differential form, synthetic differential geometry, groupoid, coboundary operator, Maurer-Cartan equation.

 


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