@article{CTGDC_2011__52_1_45_0, author = {Grandis, Marco}, title = {Singularities and regular paths (an elementary introduction to smooth homotopy)}, journal = {Cahiers de Topologie et G\'eom\'etrie Diff\'erentielle Cat\'egoriques}, eid = {2}, pages = {45--76}, publisher = {Andr\'ee CHARLES EHRESMANN}, volume = {52}, number = {1}, year = {2011}, mrnumber = {2807421}, zbl = {1237.58007}, language = {en}, url = {http://www.numdam.org/item/CTGDC_2011__52_1_45_0/} }
TY - JOUR AU - Grandis, Marco TI - Singularities and regular paths (an elementary introduction to smooth homotopy) JO - Cahiers de Topologie et Géométrie Différentielle Catégoriques PY - 2011 SP - 45 EP - 76 VL - 52 IS - 1 PB - Andrée CHARLES EHRESMANN UR - http://www.numdam.org/item/CTGDC_2011__52_1_45_0/ LA - en ID - CTGDC_2011__52_1_45_0 ER -
%0 Journal Article %A Grandis, Marco %T Singularities and regular paths (an elementary introduction to smooth homotopy) %J Cahiers de Topologie et Géométrie Différentielle Catégoriques %D 2011 %P 45-76 %V 52 %N 1 %I Andrée CHARLES EHRESMANN %U http://www.numdam.org/item/CTGDC_2011__52_1_45_0/ %G en %F CTGDC_2011__52_1_45_0
Grandis, Marco. Singularities and regular paths (an elementary introduction to smooth homotopy). Cahiers de Topologie et Géométrie Différentielle Catégoriques, Tome 52 (2011) no. 1, article no. 2, 32 p. http://www.numdam.org/item/CTGDC_2011__52_1_45_0/
[BH] Convenient categories of smooth spaces, Trans. Amer. Math. Soc., to appear. Preprint [arXiv:0807.1704]. | Zbl
and ,[Bo] Differentiability of a function and of its compositions with functions of one variable, Math. Scand. 20 (1967), 249-268. | EuDML | MR | Zbl
,[CP] On a family of topological invariants similar to homotopy groups, Rend. Istit. Mat. Univ. Trieste 30 (1998), 81-90. | MR | Zbl
and ,[Ca] Théorie élémentaire des fonctions analytiques d'une ou plusieurs variables complexes, Hermann, Paris 1961. | MR | Zbl
,[Ch] Iterated path integrals, Bull. Amer. Math. Soc. 83 (1977), 831-879. | MR | Zbl
,[Ck] The left exactness of the smooth left Puppe sequence, in New developments in differential geometry, 59-76, Kluwer Acad. Publ., Dordrecht 1996. | MR | Zbl
,[E1] Les prolongements d'une variété différentiable. I. Calcul des jets, prolongement principal. C. R. Acad. Sci. Paris 233, (1951). 598-600. | MR | Zbl
,[E2] Les prolongements d'une variété différentiable. II. L'espace des jets d'ordre de dans . C. R. Acad. Sci. Paris 233, (1951). 777-779. | MR | Zbl
,[Fr] Smooth structures, in Category Theory, Gummersbach 1981, pp. 69-81
,Smooth structures, Lect. Notes in Math. Vol. 962, Springer, Berlin 1982. | MR
,[G1] Manifolds as enriched categories, in: Categorical Topology, Prague 1988, pp.358-368, World Scientific 1989. | MR
,[G2] Cohesive categories and manifolds, Ann. Mat. Pura Appl. 157 (1990), 199-244. | MR | Zbl
,[G3] Directed Algebraic Topology, Models of non-reversible worlds, Cambridge Univ. Press, Cambridge 2009. | MR | Zbl
,[Ko] Synthetic differential geometry, Cambridge Univ. Press, Cambridge 1981. | MR | Zbl
,[Ma] Ideals of differentiable functions, Oxford Univ. Press, Oxford 1966. | MR
,[MBB] On regular presheaves and regular semi-categories, Cah. Topol. Géom. Différ. Catég. 43 (2002), 163-190. | EuDML | Numdam | MR | Zbl
, and ,[MR] Models for smooth infinitesimal analysis, Springer, Berlin 1991. | MR | Zbl
and ,[SSS] Differential twisted String and Fivebrane structures, Preprint (2009) [arXiv:0910.4001]. | MR | Zbl
, and ,[SW1] Parallel transport and functors, J. Homotopy Relat. Struct. 4 (2009), 187-244. | MR | Zbl
and ,[SW2] Smooth functors vs. differential forms, Preprint [arXiv:0802.0663]. | MR | Zbl
and ,[So] Groupes différentiels, in Differential Geometrical Methods in Mathematical Physics (Proc. Conf., Aix-en-Provence/Salamanca, 1979), Lecture Notes in Math. 836, Springer, Berlin 1980, pp. 91-128. | MR
,[Ze] The topology of the brain and visual perception, in: Topology of 3-manifolds and related topics, pp. 240-256, Prentice-Hall, Englewood Cliffs, N.J., 1962. | MR | Zbl
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