Abstract
It is shown that any smooth closed orientable manifold of dimension
Funding statement: Purvi Gupta is supported in part by a UGC CAS-II grant (Grant No. F.510/25/CAS-II/2018(SAP-I)). Rasul Shafikov is partially supported by the Natural Sciences and Engineering Research Council of Canada.
References
[1] J. F. Adams, Stable homotopy and generalised homology, Chicago Lectures in Math. University of Chicago Press, Chicago 1974. Search in Google Scholar
[2] H. Alexander, Linking and holomorphic hulls, J. Differential Geom. 38 (1993), no. 1, 151–160. 10.4310/jdg/1214454098Search in Google Scholar
[3]
H. Alexander,
Hulls of subsets of the torus in
[4] M. Arkowitz, Introduction to homotopy theory, Universitext, Springer, New York 2011. 10.1007/978-1-4419-7329-0Search in Google Scholar
[5] L. Arosio and E. F. Wold, Totally real embeddings with prescribed polynomial hulls, Indiana Univ. Math. J. 68 (2019), no. 2, 629–640. 10.1512/iumj.2019.68.7603Search in Google Scholar
[6]
V. K. Beloshapka,
The normal form of germs of four-dimensional real submanifolds in
[7] E. Bishop, Differentiable manifolds in complex Euclidean space, Duke Math. J. 32 (1965), 1–21. 10.1142/9789814415514_0025Search in Google Scholar
[8] K. Cieliebak and Y. Eliashberg, The topology of rationally and polynomially convex domains, Invent. Math. 199 (2015), no. 1, 215–238. 10.1007/s00222-014-0511-6Search in Google Scholar
[9] A. Coffman, Enumeration and normal forms of singularities in Cauchy–Riemann structures, ProQuest LLC, Ann Arbor 1997; Ph.D. thesis, The University of Chicago, Chicago 1997. Search in Google Scholar
[10] A. Coffman, Unfolding CR singularities, Mem. Amer. Math. Soc. 205 (2010), no. 962. 10.1090/S0065-9266-09-00575-4Search in Google Scholar
[11] A. V. Domrin, A description of characteristic classes of real submanifolds in complex manifolds in terms of RC-singularities, Izv. Math. 59 (1995), no. 5, 899–918. 10.1070/IM1995v059n05ABEH000039Search in Google Scholar
[12] Y. Eliashberg and N. Mishachev, Introduction to the h-principle, Grad. Stud. Math. 48, American Mathematical Society, Providence 2002. 10.1090/gsm/048Search in Google Scholar
[13]
F. Forstnerič,
Approximation by automorphisms on smooth submanifolds of
[14] F. Forstnerič, Complements of Runge domains and holomorphic hulls, Michigan Math. J. 41 (1994), no. 2, 297–308. 10.1307/mmj/1029004997Search in Google Scholar
[15]
F. Forstnerič and J.-P. Rosay,
Approximation of biholomorphic mappings by automorphisms of
[16] M. E. Gilmore, Complex Stiefel manifolds, some homotopy groups and vector fields, Bull. Amer. Math. Soc. 73 (1967), 630–633. 10.1090/S0002-9904-1967-11802-0Search in Google Scholar
[17] M. E. Gilmore, Homotopy groups of complex Stiefel manifolds, ProQuest LLC, Ann Arbor 1967; Ph.D. thesis, University of California, Berkeley 1967. Search in Google Scholar
[18] P. Gupta and R. Shafikov, Polynomially convex embedddings of even-dimensional compact manifolds, Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 21 (2020), 1649–1666. 10.2422/2036-2145.201811_008Search in Google Scholar
[19] F. R. Harvey and R. O. Wells, Holomorphic approximation on totally real submanifolds of a complex manifold, Bull. Amer. Math. Soc. 77 (1971), no. 5, 824–828. 10.1090/S0002-9904-1971-12820-3Search in Google Scholar
[20] A. Hatcher, Algebraic topology, Cambridge University Press, Cambridge 2002. Search in Google Scholar
[21]
P. T. Ho, H. Jacobowitz and P. Landweber,
Optimality for totally real immersions and independent mappings of manifolds into
[22] A. J. Izzo, No topological condition implies equality of polynomial and rational hulls, Proc. Amer. Math. Soc. 147 (2019), no. 12, 5195–5207. 10.1090/proc/14628Search in Google Scholar
[23] A. J. Izzo and E. L. Stout, Hulls of surfaces, Indiana Univ. Math. J. 67 (2018), no. 5, 2061–2087. 10.1512/iumj.2018.67.6250Search in Google Scholar
[24] S. O. Kochman, Bordism, stable homotopy and Adams spectral sequences, Fields Inst. Monogr. 7, American Mathematical Society, Providence 1996. 10.1090/fim/007Search in Google Scholar
[25] E. Løw and E. F. Wold, Polynomial convexity and totally real manifolds, Complex Var. Elliptic Equ. 54 (2009), no. 3–4, 265–281. 10.1080/17476930902759395Search in Google Scholar
[26] S. Minsker, Some applications of the Stone–Weierstrass theorem to planar rational approximation, Proc. Amer. Math. Soc. 58 (1976), 94–96. 10.1090/S0002-9939-1976-0467322-6Search in Google Scholar
[27]
S. Nemirovski and K. Siegel,
Rationally convex domains and singular Lagrangian surfaces in
[28] A. G. O’Farrell, K. J. Preskenis and D. Walsh, Holomorphic approximation in Lipschitz norms, Proceedings of the conference on Banach algebras and several complex variables (New Haven 1983), Contemp. Math. 32, American Mathematical Society, Providence (1984), 187–194. 10.1090/conm/032/769507Search in Google Scholar
[29] G. Stolzenberg, Polynomially and rationally convex sets, Acta Math. 109 (1963), 259–289. 10.1007/BF02391815Search in Google Scholar
[30] E. L. Stout, Polynomial convexity, Progr. Math. 261, Birkhäuser, Boston 2007. Search in Google Scholar
[31] D. G. Vodovoz and M. G. Zaidenberg, The number of generators in an algebra of continuous functions, Math. Notes 10 (1971), 746–748. 10.1007/BF01109037Search in Google Scholar
[32] R. O. Wells, Jr., Compact real submanifolds of a complex manifold with nondegenerate holomorphic tangent bundles, Math. Ann. 179 (1969), 123–129. 10.1007/BF01350124Search in Google Scholar
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