4-manifolds and Kirby calculus

4-manifolds: Introduction Surfaces in 4-manifolds Complex surfaces Kirby calculus: Handelbodies and Kirby diagrams Kirby calculus More examples Applications: Branched covers and resolutions Elliptic and Lefschetz fibrations Cobordisms, $h$-cobordisms and exotic ${\mathbb{R}}^{4,}$s Symplectic 4-manifolds Stein surfaces Appendices: Solutions Notation, important figures Bibliography Index.

[1]  Paul Melvin,et al.  The 3-manifold invariants of Witten and Reshetikhin-Turaev for sl(2, C) , 1991 .

[2]  S. J. Kaplan.  Constructing framed 4-manifolds with given almost framed boundaries , 1979 .

[3]  A. Sommese.  On the density of ratios of Chern numbers of algebraic surfaces , 1984 .

[4]  J. Harer.  On handlebody structures for hypersurfaces in ℂ3 and ℂP3 , 1978 .

[5]  Xiao Gang.  Surfaces Fibrees en Courbes de Genre Deux , 1985 .

[6]  N. Steenrod.  The Topology of Fibre Bundles. (PMS-14) , 1951 .

[7]  Robert E. Gompf.  Stable diffeomorphism of compact 4-manifolds , 1984 .

[8]  S. Akbulut,et al.  Branched covers of surfaces in 4-manifolds , 1980 .

[9]  Terry Fuller.  Distinguishing embedded curves in rational complex surfaces , 1998 .

[10]  M. Polyak,et al.  A geometrical presentation of the surface mapping class group and surgery , 1994 .

[11]  Robion Kirby,et al.  A calculus for framed links inS3 , 1978 .

[12]  N. Habegger,et al.  Topological Auantum Field Theories derived from the Kauffman bracket , 1995 .

[13]  Edwin E. Moise,et al.  Affine structures in 3-manifolds, V, The triangulation theorem and Hauptvermutung , 1952 .

[14]  Scharlemann's manifold is standard , 1997, math/9712255.

[15]  Robert E. Gompf.  A new construction of symplectic manifolds , 1995 .

[16]  W. Browder.  Surgery on Simply-Connected Manifolds , 1972 .

[17]  B. Moishezon.  Complex Surfaces and Connected Sums of Complex Projective Planes , 1977 .

[18]  Patrick D. Shanahan.  The Atiyah-Singer index theorem: An introduction , 1978 .

[19]  T. Ohtsuki.  Finite type invariants of integral homology 3-spheres , 1996 .

[20]  J. Cerf.  La stratification naturelle des espaces de fonctions différentiables réelles et le théorème de la pseudo-isotopie , 1970 .

[21]  S. Donaldson.  Symplectic submanifolds and almost-complex geometry , 1996 .

[22]  S. Donaldson.  Lefschetz pencils on symplectic manifolds , 1999 .

[23]  A. Kawauchi,et al.  Algebraic classification of linking pairings on 3-manifolds , 1980 .

[24]  P. Pao.  Non-linear circle actions on the 4-sphere and twisting spun knots , 1978 .

[25]  Akbulut's corks and h-cobordisms of smooth simply connected 4-manifolds , 1997, math/9712231.

[26]  Klaus Lamotke,et al.  The topology of complex projective varieties after S , 1981 .

[27]  Knots, links, and 4-manifolds , 1996, dg-ga/9612014.

[28]  Kim A. Frøyshov.  The Seiberg-Witten equations and four-manifolds with boundary , 1996 .

[29]  Robert E. Gompf.  Killing the Akbulut-Kirby 4-sphere, with relevance to the Andrews-Curtis and Schoenflies problems , 1991 .

[30]  Paul T. Norbury,et al.  Notes on Geometry and 3-Manifolds , 2001 .

[31]  James Eells,et al.  A fibre bundle description of Teichmüller theory , 1969 .

[32]  D. B. Fuks.  Homotopic topology , 1973 .

[33]  I. Shafarevich.  Basic algebraic geometry , 1974 .

[34]  S. Donaldson.  Geometry of four-manifolds , 1990 .

[35]  Daniel Ruberman.  Imbedding four-manifolds and slicing links , 1982, Mathematical Proceedings of the Cambridge Philosophical Society.

[36]  Quasipositivity as an obstruction to sliceness , 1993, math/9307233.

[37]  T. Matumoto.  Extension problem of diffeomorphisms of a 3-torus over some 4-manifolds , 1984 .

[38]  Yakov Eliashberg,et al.  Contact 3-manifolds twenty years since J. Martinet's work , 1992 .

[39]  E. Bombieri.  Canonical models of surfaces of general type , 1973 .

[40]  Z. Szabó.  Simply-connected irreducible 4-manifolds with no symplectic structures , 1998 .

[41]  Y. Eliashberg.  Classification of overtwisted contact structures on 3-manifolds , 1989 .

[42]  J. Morgan,et al.  The L[2]-moduli space and a vanishing theorem for Donaldson polynomial invariants , 1994 .

[43]  Michael H. Freedman,et al.  Topology of 4-Manifolds (PMS-39), Volume 39 , 1990 .

[44]  Selman Akbulut,et al.  A fake compact contractible 4-manifold , 1991 .

[45]  A. Stipsicz.  A note on the geography of symplectic manifolds , 1996 .

[46]  M. Teicher,et al.  Simply-connected algebraic surfaces of positive index , 1987 .

[47]  L. Rudolph.  The slice genus and the Thurston-Bennequin invariant of a knot , 1997 .

[48]  Dusa McDuff,et al.  Introduction to Symplectic Topology , 1995 .

[49]  Yukio Matsumoto.  Torus fibrations over the 2-sphere with the simplest singular fibers , 1985 .

[50]  J. Amorós.  Fundamental Groups of Compact Kähler Manifolds , 1996 .

[51]  Zhi-jie Chen.  The existence of algebraic surfaces with preassigned Chern numbers , 1991 .

[52]  D. Mcduff.  The local behaviour of holomorphic curves in almost complex 4-manifolds , 1991 .

[53]  F. Laudenbach,et al.  A note on 4-dimensional handlebodies , 1972 .

[54]  Y. Miyaoka.  The maximal number of quotient singularities on surfaces with given numerical invariants , 1984 .

[55]  D. Mcduff.  Examples of simply-connected symplectic non-Kählerian manifolds , 1984 .

[56]  W. Thurston.  Some simple examples of symplectic manifolds , 1976 .

[57]  Robert E. Gompf,et al.  Irreducible 4-manifolds need not be complex , 1993 .

[58]  Yukio Matsumoto.  LEFSCHETZ FIBRATIONS OF GENUS TWO - A TOPOLOGICAL APPROACH , 1996 .

[59]  J. Morgan.  The Seiberg-Witten equations and applications to the topology of smooth four-manifolds , 1995 .

[60]  D. Mcduff.  The structure of rational and ruled symplectic 4-manifolds , 1990 .

[61]  R. Kirby,et al.  Dedekind sums, μ-invariants and the signature cocycle , 1994 .

[62]  Charles F. Miller.  Decision Problems for Groups — Survey and Reflections , 1992 .

[63]  Selman Akbulut,et al.  An exotic 4-manifold , 1991 .

[64]  Edited Rob Kirby,et al.  Problems in Low-Dimensional Topology , 1995 .

[65]  F. Hirzebruch.  Automorphe Formen und der Satz von Riemann-Roch , 1958 .

[66]  A moduli space of exotic 4 'S , 1989 .

[67]  Emmanuel Giroux.  Une structure de contact, même tendue, est plus ou moins tordue , 1994 .

[68]  M. Freedman,et al.  A decomposition theorem for h-cobordant smooth simply-connected compact 4-manifolds , 1996 .

[69]  J. Munkres,et al.  Elementary Differential Topology. , 1967 .

[70]  R. Lathe.  Phd by thesis , 1988, Nature.

[71]  Jesse Freeman,et al.  in Morse theory, , 1999 .

[72]  J. Murakami,et al.  On a universal perturbative invariant of 3-manifolds , 1998 .

[73]  Alan H. Durfee,et al.  Fifteen characterizations of rational double points and simple critical points , 1979 .

[74]  S. Smale.  The generalized Poincaré conjecture in higher dimensions , 1960 .

[75]  J. Milnor.  Singular points of complex hypersurfaces , 1968 .

[76]  R. Stern,et al.  IMMERSED SPHERES IN 4-MANIFOLDS AND THE IMMERSED THOM CONJECTURE , 1995 .

[77]  U. Persson.  Chern invariants of surfaces of general type , 1981 .

[78]  Arnaud Beauville,et al.  Complex Algebraic Surfaces , 1996 .

[79]  Henry B. Laufer.  Normal Two-Dimensional Singularities. , 1971 .

[80]  Diffeomorphism types of genus 2 Lefschetz fibrations , 1998 .

[81]  W. Lickorish,et al.  An Introduction to Knot Theory , 1997 .

[82]  R. Kirby,et al.  Quantum invariants at the sixth root of unity , 1993 .

[83]  Y. Eliashberg.  Geometry of Low-dimensional Manifolds: Filling by holomorphic discs and its applications , 1991 .

[84]  C. Taubes.  THE SEIBERG-WITTEN INVARIANTS AND SYMPLECTIC FORMS , 1994 .

[85]  Terry C. Lawson.  h-Cobordisms between simply connected 4-manifolds , 1988 .

[86]  Yukio Matsumoto.  On $4$-manifolds fibered by Tori, II , 1982 .

[87]  J. Morgan,et al.  A product formula for the seiberg-witten invariants and the generalized thom conjecture , 1996 .

[88]  S. Donaldson.  Lefschetz Fibrations in Symplectic Geometry , 1998 .

[89]  J. Harer,et al.  Some homology lens spaces which bound rational homology balls. , 1981 .

[90]  Robert E. Gompf.  An exotic menagerie , 1993 .

[91]  Yakov Eliashberg,et al.  New applications of Luttinger’s surgery , 1994 .

[92]  S. Akbulut.  On 2-dimensional homology classes of 4-manifolds , 1977, Mathematical Proceedings of the Cambridge Philosophical Society.

[93]  Y. Eliashberg.  Unique holomorphically fillable contact structure on the 3-torus , 1996 .

[94]  J. Milnor.  Lectures on the h-cobordism theorem , 1965 .

[95]  László Fuchs,et al.  Infinite Abelian groups , 1970 .

[96]  Spin c {structures and homotopy equivalences , 1997, math/9705218.

[97]  Clifford Henry Taubes,et al.  Gauge theory on asymptotically periodic {4}-manifolds , 1987 .

[98]  J. Morgan,et al.  Homotopy K3 surfaces and mod 2 Seiberg-Witten invariants , 1997 .

[99]  J. Milnor,et al.  ON 2-SPHERES IN 4-MANIFOLDS. , 1961, Proceedings of the National Academy of Sciences of the United States of America.

[100]  Hisaaki Endo.  Meyer's signature cocycle and hyperelliptic fibrations , 2000 .

[101]  J. Harer,et al.  Handlebody decompositions of complex surfaces , 1986 .

[102]  B. Trace.  On attaching $3$-handles to a $1$-connected $4$-manifold. , 1982 .

[103]  Algebraic surfaces and Seiberg-Witten invariants , 1995, alg-geom/9502026.

[104]  Chih-Han Sah,et al.  Symmetric bilinear forms and quadratic forms , 1972 .

[105]  Ronnie Lee,et al.  Representing homology classes by locally flat surfaces of minimum genus , 1997 .

[106]  N. Elkies.  A characterization of the Z^n lattice , 1999, math/9906019.

[107]  P. Lisca.  Symplectic fillings and positive scalar curvature , 1998, math/9807188.

[108]  Ding Fan.  Smooth structures on some open 4-manifolds , 1997 .

[109]  Tian-Jun Li.  SMOOTHLY EMBEDDED SPHERES IN SYMPLECTIC 4-MANIFOLDS , 1999 .

[110]  On the Donaldson polynomials of elliptic surfaces , 1994 .

[111]  P. Kronheimer,et al.  The Genus of Embedded Surfaces in the Projective Plane , 1994 .

[112]  F. Hirzebruch.  The signature of ramified coverings , 1969 .

[113]  A. Stipsicz.  Simply connected 4-manifolds near the Bogomolov-Miyaoka-Yau line , 1998 .

[114]  R. Ho.  Algebraic Topology , 2022 .

[115]  N. Lu.  A simple proof of the fundamental theorem of Kirby calculus on links , 1992 .

[116]  W. Ebeling.  An example of two homeomorphic, nondiffeomorphic complete intersection surfaces , 1990 .

[117]  Periodic ends and knot concordance , 1989 .

[118]  E. Groves.  A Dissertation ON , 1928 .

[119]  R. Mandelbaum.  DECOMPOSING ANALYTIC SURFACES , 1979 .

[120]  H. Whitney,et al.  CLASSIFICATION OF ORIENTED SPHERE BUNDLES OVER A 4-COMPLEX , 1959 .

[121]  H. Bass,et al.  The Smith conjecture , 1984 .

[122]  Robert E. Gompf.  Sums of elliptic surfaces , 1991 .

[123]  Y. Eliashberg.  Symplectic geometry of plurisubharmonic functions , 1997 .

[124]  Robert E. Gompf.  Infinite families of casson handles and topological disks , 1984 .

[125]  A. Kas.  Complex Analysis and Algebraic Geometry: On the Deformation Types of Regular Elliptic Surfaces , 1977 .

[126]  M. Scharlemann.  Constructing strange manifolds with the dodecahedral space , 1976 .

[127]  V. Turaev.  Quantum Invariants of Knots and 3-Manifolds , 1994, hep-th/9409028.

[128]  S. Donaldson.  An application of gauge theory to four-dimensional topology , 1983 .

[129]  Handlebody construction of Stein surfaces , 1998, math/9803019.

[130]  M. Freedman,et al.  A universal smoothing of four-space , 1986 .

[131]  Rational blowdowns of smooth 4-manifolds , 1995, alg-geom/9505018.

[132]  D. Kotschick.  The Seiberg-Witten invariants of symplectic four-manifolds , 1996 .

[133]  Tian-Jun Li,et al.  Symplectic structure on ruled surfaces and a generalized adjunction formula , 1995 .

[134]  B. Wajnryb.  A simple presentation for the mapping class group of an orientable surface , 1983 .

[135]  Y. Eliashberg.  TOPOLOGICAL CHARACTERIZATION OF STEIN MANIFOLDS OF DIMENSION >2 , 1990 .

[136]  Vector bundles and $SO(3)$ invariants for elliptic surfaces II: The case of even fiber degree , 1993, alg-geom/9307003.

[137]  Loring W. Tu,et al.  Differential forms in algebraic topology , 1982, Graduate texts in mathematics.

[138]  S. Yau,et al.  Calabi's conjecture and some new results in algebraic geometry. , 1977, Proceedings of the National Academy of Sciences of the United States of America.

[139]  Michael H. Freedman,et al.  The topology of four-dimensional manifolds , 1982 .

[140]  J. Milnor.  On Manifolds Homeomorphic to the 7-Sphere , 1956 .

[141]  Joe W. Harris,et al.  Principles of Algebraic Geometry , 1978 .

[142]  Zyun'iti Iwase.  Good torus fibrations with twin singular fibers , 1984 .

[143]  J. Morgan,et al.  Smooth Four-Manifolds and Complex Surfaces , 1994 .

[144]  Terry Fuller.  Generalized nuclei of complex surfaces , 1999 .

[145]  M. Ue,et al.  On the diffeomorphism types of elliptic surfaces with multiple fibers , 1986 .

[146]  F. Quinn.  Ends of maps. III. Dimensions 4 and 5 , 1982 .

[147]  C. Taubes.  Counting pseudo-holomorphic submanifolds in dimension 4 , 1996 .

[148]  Z. Szabó.  Irreducible four-manifolds with small Euler characteristics , 1996 .