Available in electronic format
Available in print format
Bulletin of the American Mathematical Society
Bulletin of the American Mathematical Society
ISSN 1088-9485(e) ISSN 0273-0979(p)
     

A theory of characteristic currents associated with a singular connection

Author(s): Reese Harvey; H. Blaine Lawson Jr.
Journal: Bull. Amer. Math. Soc. 31 (1994), 54-63.
MSC (1991): Primary 53C07, 49Q15; Secondary 58H99, 57R20
MathSciNet review: 1254076
Retrieve article in: PDF

References | Similar articles | Additional information

References:

[AH]
M. F. Atiyah and F. Hirzebruch, The Riemann-Roch theorem for analytic embeddings, Topology \textbf{1} (1962), 151--166. MR 148084
[BGS1]
J.-M. Bismut, H. Gillet, and C. Soul\'e, Analytic torsion and holomorphic determinant bundles. {\rm I, II, III}, Comm. Math. Physics \textbf{115} (1988), 49--78, 79--126, 301--351. MR
[BGS2]
J.-M. Bismut, H. Gillet, and C. Soul\'e, Bott-Chern currents and complex immersions, Duke Math. J. \textbf{60} (1990), 255--284. MR 1047123
[BGS3]
J.-M. Bismut, H. Gillet, and C. Soul\'e, Complex immersions and Arakelov geometry, Grothendieck Fetschrift I, Birkh\"auser, Boston, 1990, pp.~249--331. MR 1086887
[BV]
N. Berline and M. Vergne, A computation of the equivariant index of the Dirac operator, Bull. Soc. Math. France \textbf{113} (1985), 305--345. MR 834043
[C1]
S. Chern, A simple intrinsic proof of the Gauss-Bonnet formula for closed Riemannian manifolds, Ann. of Math. (2) \textbf{45} (1944), 747--752. MR 11027
[C2]
S. Chern, On the curvature integra in a Riemannian manifold, Ann. of Math. (2) \textbf{46} (1945), 674--684. MR 14760
[F]
H. Federer, Geometric measure theory, Springer-Verlag, New York, 1969. MR 257325
[Fu]
W. Fulton, \emph{Intersection theory}, Springer-Verlag, Berlin and Heidelberg, 1984. MR 732620
[HL1]
F. R. Harvey and H. B. Lawson, Jr., {\rm A theory of characteristic currents associated with a singular connection}, Ast\'erisque \textbf{213} (1993), 1--268. MR 1230025
[HL2]
F. R. Harvey and H. B. Lawson, Jr., Geometric residue theorems, MSRI Preprint, 1993, pp.~1--53. MR
[HL3]
F. R. Harvey and H. B. Lawson, Jr., A theory of characteristic currents associated with a singular connection --- Part {\rm II}, in preparation. MR
[HP]
F. R. Harvey and J. Polking, Fundamental solutions in complex analysis, Part \RM I, Duke Math. J. \textbf{46} (1979), 253--300. MR 534054
[HS]
F. R. Harvey and S. Semmes, Zero divisors of atomic functions, Ann. of Math. (2) \textbf{135} (1992), 567--600. MR 1166645
[M1]
R. MacPherson, \emph{Singularities of vector bundle maps}, Lecture Notes in Math., vol. 192, Springer-Verlag, New York, 1971 pp.~316--318. MR
[M2]
R. MacPherson, \emph{Generic vector bundle maps}, Academic Press, New York, 1973 pp.~165--175. MR 339199
[MQ]
V. Mathai and D. Quillen, Superconnections, Thom classes, and equivariant differential forms, Topology \textbf{25} (1986), 85--110. MR 836726
[MW]
M. Micallef and J. Wolfson, The second variation of area of minimal surfaces in four-manifolds, Math. Ann. \textbf{295} (1993), 245--267. MR 1202392
[Q]
D. Quillen, Superconnections and the Chern character, Topology \textbf{24} (1985), 89--95. MR 790678
[R]
F. Ronga, \emph{Le calcul de la classe de cohomologie duale a $\bar {\Sigma }^k$\<}, Lecture Notes in Math., vol. 192, Springer-Verlag, New York, 1971 pp.~313--315. MR 293648
[W1]
S. Webster, Minimal surfaces in a K\"ahler surface, J. Differential Geom. \textbf{20} (1984), 463--470. MR 788290
[W2]
S. Webster, The Euler and Pontrjagin numbers of an $n$-manifold in $\BC ^n$, Comment. Math. Helv. \textbf{60} (1985), 193--216. MR 800003
[W3]
S. Webster, On the relation between Chern and Pontrjagin numbers, Contemp. Math. \textbf{49} (1986), 135--143. MR 833810
[Wo]
J. Wolfson, Minimal surfaces in K\"ahler surfaces and Ricci curvature, J. Differential Geom. \textbf{29} (1989), 281--294. MR 982175
[Z1]
J. Zweck, Chern currents of singular connections associated with a section of a compactified bundle, 1--40 (to appear). MR 1355402
[Z2]
J. Zweck, Euler and Pontrjagin currents of a section of a compactified real bundle, 1--32 (to appear). MR 1353060

Similar Articles:

Retrieve articles in Bulletin of the American Mathematical Society with MSC (1991): 53C07, 49Q15, 58H99, 57R20

Retrieve articles in all Journals with MSC (1991): 53C07, 49Q15, 58H99, 57R20


Additional Information:

DOI: 10.1090/S0273-0979-1994-00497-5
PII: S 0273-0979(1994)00497-5