Singularities of spaces of flat bundles over complex manifolds
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- by B. Wong PDF
- Trans. Amer. Math. Soc. 231 (1977), 451-461 Request permission
Abstract:
We use Fox differential calculus on free group to study the singularities of complex analytic varieties arising from flat bundles over complex manifolds. Criteria of regularity in terms of cohomology of the fundamental group of the underlying manifold are established.References
- Karl W. Gruenberg, Cohomological topics in group theory, Lecture Notes in Mathematics, Vol. 143, Springer-Verlag, Berlin-New York, 1970. MR 0279200
- R. C. Gunning, Lectures on vector bundles over Riemann surfaces, University of Tokyo Press, Tokyo; Princeton University Press, Princeton, N.J., 1967. MR 0230326
- R. C. Gunning, Lectures on complex analytic varieties: The local parametrization theorem, Mathematical Notes, Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 1970. MR 0273060
- R. C. Gunning, Local moduli for complex analytic vector bundles, Math. Ann. 195 (1971), 51–78. MR 293653, DOI 10.1007/BF02059415
- R. C. Gunning, Analytic structures on the space of flat vector bundles over a compact Riemann surface, Several complex variables, II (Proc. Internat. Conf., Univ. Maryland, College Park, Md., 1970) Lecture Notes in Math., Vol. 185, Springer, Berlin, 1971, pp. 47–62. MR 0338464
- Harald Holmann, Quotienten komplexer Räume, Math. Ann. 142 (1960/61), 407–440 (German). MR 120665, DOI 10.1007/BF01450934
- Roger C. Lyndon, Cohomology theory of groups with a single defining relation, Ann. of Math. (2) 52 (1950), 650–665. MR 47046, DOI 10.2307/1969440
- M. S. Narasimhan and C. S. Seshadri, Holomorphic vector bundles on a compact Riemann surface, Math. Ann. 155 (1964), 69–80. MR 166799, DOI 10.1007/BF01350891
- Richard S. Palais, On the existence of slices for actions of non-compact Lie groups, Ann. of Math. (2) 73 (1961), 295–323. MR 126506, DOI 10.2307/1970335
- Richard S. Palais, The classification of $G$-spaces, Mem. Amer. Math. Soc. 36 (1960), iv+72. MR 0177401
- K. Stein, On factorization of holomorphic mappings, Proc. Conf. Complex Analysis (Minneapolis, 1964) Springer, Berlin, 1965, pp. 1–7. MR 0178161
- Karl Stein, Maximale holomorphe und meromorphe Abbildungen. I, Amer. J. Math. 85 (1963), 298–315 (German). MR 152676, DOI 10.2307/2373216
- André Weil, Remarks on the cohomology of groups, Ann. of Math. (2) 80 (1964), 149–157. MR 169956, DOI 10.2307/1970495 B. Wong, Thesis, Princeton Univ., 1973 (R. C. Gunning, superviser).
Additional Information
- © Copyright 1977 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 231 (1977), 451-461
- MSC: Primary 32C40
- DOI: https://doi.org/10.1090/S0002-9947-1977-0473227-2
- MathSciNet review: 0473227