#### Volume 20, issue 1 (2016)

 Recent Issues
 The Journal About the Journal Editorial Board Subscriptions Editorial Interests Editorial Procedure Submission Guidelines Submission Page Ethics Statement ISSN (electronic): 1364-0380 ISSN (print): 1465-3060 Author Index To Appear Other MSP Journals
On the Hodge conjecture for $q$–complete manifolds

### Franc Forstnerič, Jaka Smrekar and Alexandre Sukhov

Geometry & Topology 20 (2016) 353–388
##### Bibliography
 1 A Andreotti, T Frankel, The Lefschetz theorem on hyperplane sections, Ann. of Math. 69 (1959) 713 MR0177422 2 A Andreotti, R Narasimhan, A topological property of Runge pairs, Ann. of Math. 76 (1962) 499 MR0140714 3 A Andreotti, F Norguet, Cycles of algebraic manifolds and ∂∂–cohomology, Ann. Scuola Norm. Sup. Pisa 25 (1971) 59 MR0288314 4 M F Atiyah, F Hirzebruch, Vector bundles and homogeneous spaces, Proc. Sympos. Pure Math. 3, Amer. Math. Soc. (1961) 7 MR0139181 5 M F Atiyah, F Hirzebruch, Analytic cycles on complex manifolds, Topology 1 (1962) 25 MR0145560 6 E Ballico, F Catanese, C Ciliberto, editors, Classification of irregular varieties: minimal models and abelian varieties, 1515, Springer (1992) MR1180332 7 W Barth, Der Abstand von einer algebraischen Mannigfaltigkeit im komplex-projektiven Raum, Math. Ann. 187 (1970) 150 MR0268181 8 G E Bredon, Topology and geometry, 139, Springer (1993) MR1224675 9 V M Buhštaber, Modules of differentials of the Atiyah–Hirzebruch spectral sequence, II, Mat. Sb. 83 (1970) 61 MR0300284 10 M Colţoiu, q–convexity : a survey, from: "Complex analysis and geometry" (editors V Ancona, E Ballico, R M Mirò-Roig, A Silva), Pitman Res. Notes Math. Ser. 366, Longman, Harlow (1997) 83 MR1477441 11 M Cornalba, P Griffiths, Analytic cycles and vector bundles on non-compact algebraic varieties, Invent. Math. 28 (1975) 1 MR0367263 12 P Deligne, The Hodge conjecture, from: "The millennium prize problems" (editors J Carlson, A Jaffe, A Wiles), Clay Math. Inst. (2006) 45 MR2238273 13 J P Demailly, Cohomology of q–convex spaces in top degrees, Math. Z. 204 (1990) 283 MR1055992 14 J P Demailly, Analytic methods in algebraic geometry, 1, International Press (2012) MR2978333 15 S Donaldson, On the existence of symplectic submanifolds, from: "Contact and symplectic geometry" (editor C B Thomas), Publ. Newton Inst. 8, Cambridge Univ. Press (1996) 307 MR1432468 16 S K Donaldson, Symplectic submanifolds and almost-complex geometry, J. Differential Geom. 44 (1996) 666 MR1438190 17 A Dor, Immersions and embeddings in domains of holomorphy, Trans. Amer. Math. Soc. 347 (1995) 2813 MR1282885 18 A Douady, Cycles analytiques (d’après M F Atiyah et F Hirzebruch), from: "Séminaire Bourbaki 1961∕1962 (Exposé 223)", W. A. Benjamin (1966) MR1611206 19 B Drinovec Drnovšek, F Forstnerič, Holomorphic curves in complex spaces, Duke Math. J. 139 (2007) 203 MR2352132 20 B Drinovec-Drnovšek, F Forstnerič, Approximation of holomorphic mappings on strongly pseudoconvex domains, Forum Math. 20 (2008) 817 MR2445119 21 B Drinovec Drnovšek, F Forstnerič, Strongly pseudoconvex domains as subvarieties of complex manifolds, Amer. J. Math. 132 (2010) 331 MR2654777 22 O Forster, Plongements des variétés de Stein, Comment. Math. Helv. 45 (1970) 170 MR0269880 23 F Forstnerič, Noncritical holomorphic functions on Stein manifolds, Acta Math. 191 (2003) 143 MR2051397 24 F Forstnerič, Holomorphic flexibility properties of complex manifolds, Amer. J. Math. 128 (2006) 239 MR2197073 25 F Forstnerič, Stein manifolds and holomorphic mappings: the homotopy principle in complex analysis, 56, Springer (2011) MR2975791 26 F Forstnerič, J Globevnik, Discs in pseudoconvex domains, Comment. Math. Helv. 67 (1992) 129 MR1144617 27 H Grauert, Analytische Faserungen über holomorph-vollständigen Räumen, Math. Ann. 135 (1958) 263 MR0098199 28 H Grauert, On Levi’s problem and the imbedding of real-analytic manifolds, Ann. of Math. 68 (1958) 460 MR0098847 29 H Grauert, Une notion de dimension cohomologique dans la théorie des espaces complexes, Bull. Soc. Math. France 87 (1959) 341 MR1505124 30 H Grauert, Theory of q–convexity and q–concavity, from: "Several complex variables, VII" (editors H Grauert, T Peternell, R Remmert), Encyclopaedia Math. Sci. 74, Springer (1994) 259 MR1326623 31 M L Green, Infinitesimal methods in Hodge theory, from: "Algebraic cycles and Hodge theory" (editors A Albano, F Bardelli), Lecture Notes in Math. 1594, Springer, Berlin (1994) 1 MR1335239 32 P Griffiths, J Harris, On the Noether–Lefschetz theorem and some remarks on codimension-two cycles, Math. Ann. 271 (1985) 31 MR779603 33 A Grothendieck, Hodge’s general conjecture is false for trivial reasons, Topology 8 (1969) 299 MR0252404 34 H A Hamm, Zur Homotopietyp Steinscher Räume, J. Reine Angew. Math. 338 (1983) 121 MR684017 35 H A Hamm, Zum Homotopietyp q–vollständiger Räume, J. Reine Angew. Math. 364 (1986) 1 MR817633 36 G M Henkin, J Leiterer, Andreotti–Grauert theory by integral formulas, 74, Birkhäuser (1988) 270 MR986248 37 W V D Hodge, The topological invariants of algebraic varieties, from: "Proceedings of the International Congress of Mathematicians, I", Amer. Math. Soc. (1952) 182 MR0046075 38 C U Jensen, Les foncteurs dérivés de et leurs applications en théorie des modules, 254, Springer (1972) MR0407091 39 B Jöricke, Envelopes of holomorphy and holomorphic discs, Invent. Math. 178 (2009) 73 MR2534093 40 S Kaliman, M Zaĭdenberg, A tranversality theorem for holomorphic mappings and stability of Eisenman–Kobayashi measures, Trans. Amer. Math. Soc. 348 (1996) 661 MR1321580 41 K Kodaira, D C Spencer, Divisor class groups on algebraic varieties, Proc. Nat. Acad. Sci. USA 39 (1953) 872 MR0063122 42 W S Massey, Singular homology theory, 70, Springer (1980) MR569059 43 J Milnor, On axiomatic homology theory, Pacific J. Math. 12 (1962) 337 MR0159327 44 T Ohsawa, Completeness of noncompact analytic spaces, Publ. Res. Inst. Math. Sci. 20 (1984) 683 MR759689 45 M Peternell, q–completeness of subsets in complex projective space, Math. Z. 195 (1987) 443 MR895316 46 M Schneider, Über eine Vermutung von Hartshorne, Math. Ann. 201 (1973) 221 MR0357858 47 G Sorani, Omologia degli spazi q–pseudoconvessi, Ann. Scuola Norm. Sup. Pisa 16 (1962) 299 MR0157005 48 C Soulé, C Voisin, Torsion cohomology classes and algebraic cycles on complex projective manifolds, Adv. Math. 198 (2005) 107 MR2183252 49 E H Spanier, Algebraic topology, Springer (1981) MR666554 50 B Totaro, Torsion algebraic cycles and complex cobordism, J. Amer. Math. Soc. 10 (1997) 467 MR1423033 51 S Trivedi, Stratified transversality of holomorphic maps, Internat. J. Math. 24 (2013) 1350106, 12 MR3158578 52 C A Weibel, An introduction to homological algebra, 38, Cambridge Univ. Press (1994) MR1269324