Abstract
This paper first appeared in a collection of lecture notes which were distributed at the A.M.S. Summer Institute on Differential Geometry, held at Stanford in 1973. Since then it has been (and remains) the authors' intention to make available a more detailed version. But, in the mean time, we continued to receive requests for the original notes. Moreover, the secondary invariants we discussed have recently arisen in some new contexts, e.g. in physics and in the work of Cheeger and Gromov on "collapse" (which was the subject of the first author's lectures at the Special Year). For these reasons we decided to finally publish the notes, albeit in their original form.
Keywords
- Vector Bundle
- Cohomology Class
- Normal Bundle
- Lens Space
- Differential Character
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Partially supported by Alfred P. Sloan Foundation and N.S.F. Grant GP 31359X-1.
Partially supported by N.S.F. Grant PO 29743002.
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References
W. Ambrose and I. M. Singer, "A theorem on Holonomy," Trans. Amer. Math. Soc. 75 (1953), 428–443.
M. F. Atiyah, "Characters and cohomology of finite groups," Pub. Math. I.H.E.S., 9, (1961).
M. F. Atiyah, V. Patodi and I. M. Singer, "Spectral asymmetry and Riemannian geometry I," Math. Proc. Camb. Phil. Soc. (1975), 43–69.
R. Bott, "On a topological obstruction to integrability," Proc. Internat. Congress Math. (Nice 1970), Vol. 1, Gauthier-Villars, Paris, 1971, 27–36.
R. Bott, A. Haefliger, "On characteristic classes of Γ-foliations," Bull. A.M.S. Vol. 78, No. 6, 1039–1044.
R. Bott and J. Heitsch, "A remark on the integral cohomology of BΓq," Topology Vol. 9, No. 2, 1972.
J. Cheeger, "Multiplication of differential characters," Instituto Nazionale di Alta Mathematica, Symposia Mathematica, Vol. XI, (1973), 441–445.
S. S. Chern, "A simple intrinsic proof of the Gauss Bonnet formula, for closed Riemannian manifolds," Ann. of Math., Vol. 45 (1944), 747–752.
S. S. Chern and J. Simons, "Characteristic forms and geometric invariants," Ann. of Math., 99 (1974) 48–69.
H. S. M. Coxeter, "The functions of Schlafli and Lobatschevsky," Quart. J. Math., 6, (1935), 13–29.
P. Hilton and S. Wylie, "Homology theory," Cambridge University Press, 1960.
M. Kervaire, "Extension d'un théorèm de G. de Rham et expression de I'invariant de Hopf une integrale," C.R. Acad. Sci. Paris 237, (1953), 1486–1488.
J. Millson, Ph.D. thesis, Berkeley, 1973.
C. Moore, "Extension and low dimensional cohomology of locally compact groups, I," Trans. Am. Math. Soc. 113 (1964), 40–63.
H. S. Narasinhan and S. Ramanan, "Existence of universal connections," Am. J. Math., 83, (1961), 563–572; 85, (1963), 223–231.
L. Schlafli, "On the multiple integral ∝∝...∝ dxdy...dz whose limits are p1 = a1x + b1t =...+ h1z > 0, p2 > 0,...,pn > 0, and x2 + y2 +...+ z2 < 1, Quart. J. Math. 3, (1860), 54–68, 97–108.
J. Simons, "Characteristic forms and transgression II: Characters associated to a connection," Preprint.
D. Wigner, Ph.D. Thesis, Berkeley, 1972.
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© 1985 Springer-Verlag
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Cheeger, J., Simons, J. (1985). Differential characters and geometric invariants. In: Geometry and Topology. Lecture Notes in Mathematics, vol 1167. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0075216
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DOI: https://doi.org/10.1007/BFb0075216
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