DIFFERENT FACES OF GEOMETRY
CONTENT REFINED SEIBERG–WITTEN INVARIANTS THE MONOPOLE MAP ENTER STABLE HOMOTOPY SOME EQUIVARIANT TOPOLOGY TOPOLOGY OF THE MONOPOLE MAP THE CASE THE CASE THE CASE THE CASE SUMMARY KÄHLER, SYMPLECTIC, AND ALMOST COMPLEX MANIFOLDS SOME STABLE COHOMOTOPY GROUPS INTERMEZZO EQUIVARIANT TRANSVERSALITY A VARIANT ON THE EILENBERG-SWINDLE EQUIVARIANCE TO THE RESCUE UNIVERSES TO THE RESCUE ON THE USAGE OF SPECTRA I WHY DO UNIVERSES WORK? ON THE USAGE OF SPECTRA II GLUING RESULTS 1 2 3 4 4 1 4 2 4 3 4 4 4 5 5 6 7 7 1 7 2 7 3 7 4 7 5 7 6 7 7 8 GLUING BASIC EXAMPLES WITH TRIVIAL STATE TRANSITIONS MORE COMPLICATED EXAMPLE TIGHTNESS AND FILLABILITY REFERENCES 8 1 8 2 9 9 1 9 2 9 3 10 1 1 1 1 2 1 3 1 4 1 5 1 6 2 2 1 2 2 2 3 3 3 1 3 2 4 4 1 4 2 4 3 4 4 5 5 1 5 2 5 3 ASYMPTOTIC CONVEX GEOMETRY SHORT OVERVIEW INTRODUCTION ASYMPTOTIC CONVEX GEOMETRY ISOMORPHIC ISOPERIMETRIC INEQUALITIES AND CONCENTRATION OF MEASURE DVORETZKY TYPE THEOREMS THE AND PISIER’S INEQUALITY LOW M*-ESTIMATE AND THE QUOTIENT OF SUBSPACE THEOREM COORDINATE THEORY COVERING RESULTS GLOBAL THEORY AND ASYMPTOTIC FORMULAS CLASSICAL CONVEXITY CONNECTED TO THE ASYMPTOTIC THEORY BRUNN–MINKOWSKI INEQUALITY: CLASSICAL PROOFS AND FUNCTIONAL FORMS GEOMETRIC INEQUALITIES OF HYPERBOLIC TYPE VOLUME PRESERVING TRANSFORMATIONS EXTREMAL PROBLEMS AND ISOTROPIC POSITIONS CLASSICAL POSITIONS OF CONVEX BODIES ISOTROPIC POSITION AND THE SLICING PROBLEM BRASCAMP–LIEB INEQUALITY AND ITS REVERSE FORM SHARP GEOMETRIC INEQUALITIES STUDY OF GEOMETRIC PROBABILITIES ASYMPTOTIC RESULTS WITH A CLASSICAL CONVEXITY FLAVOR CLASSICAL SYMETRIZATIONS ISOMORPHIC SYMMETRIZATION ADDITIONAL INFORMATION IN THE SPIRIT OF GEOMETRIC FUNCTIONAL ANALYSIS BANACH–MAZUR DISTANCE ESTIMATES RANDOM SPACES REFERENCES SINGULARITIES OF SPECIAL LAGRANGIAN SUBMANIFOLDS INTRODUCTION SPECIAL LAGRANGIAN GEOMETRY BACKGROUND FROM SYMPLECTIC GEOMETRY 1 2 2 1 2 2 2 3 2 4 2 5 2 6 2 7 3 3 1 3 2 3 3 4 4 1 4 2 4 3 4 4 4 5 5 5 1 5 2 6 6 1 6 2 1 2 2 1 1 2 3 4 5 6 7 8 9 10 11 AMOEBAS OF ALGEBRAIC VARIETIES AND TROPICAL GEOMETRY PART 1 AMOEBAS DEFINITION AND BASIC PROPERTIES OF AMOEBAS DEFINITIONS AMOEBAS AT INFINITY AMOEBAS OF HYPERSURFACES: CONCAVITY AND TOPOLOGY OF THE COMPLEMENT AMOEBAS IN HIGHER CODIMENSION: CONCAVITY AMOEBAS IN HIGHER CODIMENSION: TOPOLOGY OF THE COMPLEMENT ANALYTIC TREATMENT OF AMOEBAS THE RONKIN FUNCTION THE SPINE OF AMOEBA SPINE OF AMOEBAS AND SOME FUNCTIONS ON THE SPACE OF COMPLEX POLYNOMIALS GEOMETRY OF THE MONGE–AMPÈRE MEASURE AND THE SYMPLECTIC VOLUME THE AREA OF A PLANAR AMOEBA SOME APPLICATIONS OF AMOEBAS THE FIRST PART OF HILBERT’S 16TH PROBLEM RELATION TO AMOEBAS: THE REAL PART AS A SUBSET OF THE CRITICAL LOCUS OF AND THE LOGARITHMIC GAUSS MAP COMPACTIFICATION: A TORIC VARIETY ASSOCIATED TO A HYPERSURFACE IN MAXIMALITY CONDITION FOR CURVES IN THE PLANE A HIGHER-DIMENSIONAL CASE AMOEBAS AND DIMERS PART 2 TROPICAL GEOMETRY TROPICAL DEGENERATION AND THE LIMITS OF AMOEBAS TROPICAL ALGEBRA PATCHWORKING AS TROPICAL DEGENERATION LIMIT SET OF AMOEBAS TROPICAL VARIETIES AND NON-ARCHIMEDEAN AMOEBAS CALCULUS OF TROPICAL CURVES IN DEFINITIONS DEGREE, GENUS AND THE TROPICAL RIEMANN–ROCH FORMULA 3 3 3 4 3 5 3 6 3 7 4 4 1 4 2 4 3 4 4 5 5 1 5 2 ENUMERATIVE TROPICAL GEOMETRY IN ENUMERATIVE TROPICAL GEOMETRY IN (AND HIGHER DIMENSION) COMPLEX AND REAL TROPICAL CURVES REFERENCES HEEGAARD DIAGRAMS AND HOLOMORPHIC DISKS INTRODUCTION SOME BACKGROUND ON FLOER HOMOLOGY STRUCTURE OF THIS PAPER FURTHER REMARKS THE CONSTRUCTION HEEGAARD FLOER HOMOLOGY FOR RATIONAL HOMOLOGY THREE-SPHERES AN EXAMPLE ALGEBRA MANIFOLDS WITH MAPS INDUCED BY COBORDISMS DOUBLY-POINTED HEEGAARD DIAGRAMS AND KNOT INVARIANTS BASIC PROPERTIES LONG EXACT SEQUENCES GRADINGS MAPS ON EXAMPLES INTERSECTION FORM BOUNDS FOUR-MANIFOLD INVARIANTS KNOTS IN KNOT FLOER HOMOLOGY CALCULATIONS OF KNOT FLOER HOMOLOGY KNOT FLOER HOMOLOGY AND THE SEIFERT GENUS THE FOUR-BALL GENUS UNKNOTTING NUMBERS PROBLEMS AND QUESTIONS REFERENCES 5 3 5 4 5 5 1 1 1 1 2 1 3 2 2 1 2 2 2 3 2 4 2 5 2 6 3 3 1 3 2 3 3 3 4 3 5 3 6 4 4 1 4 2 4 3 4 4 4 5 5 EXACT LAGRANGIAN SUBMANIFOLDS IN AND THE GRADED KRONECKER QUIVER INTRODUCTION THE DONALDSON–FUKAYA CATEGORY TRIANGULATED CATEGORIES THE GRADED KRONECKER QUIVER PROOF OF THEOREM REFERENCES THE CONSTRUCTION PROBLEM IN KÄHLER GEOMETRY 1 2 3 4 5