ALGORITHMIC TOPOLOGY AND CLASSIFICATION OF 3-MANIFOLDS
CONTENTS SIMPLE AND SPECIAL POLYHEDRA SPINES OF 3-MANIFOLDS COLLAPSING SPINES SPECIAL SPINES SPECIAL POLYHEDRA AND SINGULAR TRIANGULATIONS ELEMENTARY MOVES ON SPECIAL SPINES MOVES ON SIMPLE POLYHEDRA 2-CELL REPLACEMENT LEMMA BUBBLE MOVE MARKED POLYHEDRA SPECIAL POLYHEDRA WHICH ARE NOT SPINES VARIOUS NOTIONS OF EQUIVALENCE FOR POLYHEDRA MOVES ON ABSTRACT SIMPLE POLYHEDRA HOW TO HIT THE TARGET WITHOUT INVERSE U-TURNS ZEEMAN’S COLLAPSING CONJECTURE COMPLEXITY THEORY OF 3-MANIFOLDS WHAT IS THE COMPLEXITY OF A 3-MANIFOLD? ALMOST SIMPLE POLYHEDRA DE?NITION AND ESTIMATION OF THE COMPLEXITY PROPERTIES OF COMPLEXITY CONVERTING ALMOST SIMPLE SPINES INTO SPECIAL ONES THE FINITENESS PROPERTY THE ADDITIVITY PROPERTY CLOSED MANIFOLDS OF SMALL COMPLEXITY ENUMERATION PROCEDURE SIMPLI?CATION MOVES MANIFOLDS OF COMPLEXITY ?6 GRAPH MANIFOLDS OF WALDHAUSEN PROPERTIES OF GRAPH MANIFOLDS MANIFOLDS OF COMPLEXITY ?8 HYPERBOLIC MANIFOLDS HYPERBOLIC MANIFOLDS OF COMPLEXITY 9 LOWER BOUNDS OF THE COMPLEXITY LOGARITHMIC ESTIMATES COMPLEXITY OF HYPERBOLIC 3-MANIFOLDS MANIFOLDS HAVING SPECIAL SPINES WITH ONE 2-CELL HAKEN THEORY OF NORMAL SURFACES BASIC NOTIONS AND HAKEN’S SCHEME THEORY OF NORMAL CURVES NORMAL CURVES AND NORMAL EQUATIONS FUNDAMENTAL SOLUTIONS AND FUNDAMENTAL CURVES GEOMETRIC SUMMATION AN ALTERNATIVE APPROACH TO THE THEORY OF NORMAL CURVES NORMAL SURFACES IN 3-MANIFOLDS INCOMPRESSIBLE SURFACES NORMAL SURFACES IN 3-MANIFOLDS WITH BOUNDARY PATTERN NORMALIZATION PROCEDURE FUNDAMENTAL SURFACES NORMAL SURFACES IN HANDLE DECOMPOSITIONS APPLICATIONS OF THE THEORY OF NORMAL SURFACES EXAMPLES OF ALGORITHMS BASED ON HAKEN’S THEORY RECOGNITION OF SPLITTABLE LINKS GETTING RID OF CLEAN DISC PATCHES RECOGNIZING THE UNKNOT AND CALCULATING THE GENUS OF A CIRCLE IN THE BOUNDARY OF A 3-MANIFOLD IS M 3 IRREDUCIBLE AND BOUNDARY IRREDUCIBLE? IS A PROPER SURFACE INCOMPRESSIBLE AND BOUNDARY INCOMPRESSIBLE? IS M 3 SU?CIENTLY LARGE? CUTTING 3-MANIFOLDS ALONG SURFACES NORMAL SURFACES AND SPINES TRIANGULATIONS VS HANDLE DECOMPOSITIONS ALGORITHMIC RECOGNITION OF S3 LINKS IN A 3-BALL COMPRESSING DISCS AND ONE-LEGGED CROWNS THIN POSITION OF LINKS THE RUBINSTEIN THEOREM 2-NORMAL SURFACES PROOF OF THE RUBINSTEIN THEOREM THE ALGORITHM CLASSI?CATION OF HAKEN 3-MANIFOLDS MAIN THEOREM THE WALDHAUSEN THEOREM DEFORMING HOMOTOPY EQUIVALENCES OF SURFACES DEFORMING HOMOTOPY EQUIVALENCES OF 3-MANIFOLDS TO HOMEOMORPHISMS FINITENESS PROPERTIES FOR SURFACES TWO REFORMULATIONS OF THE RECOGNITION THEOREM ABSTRACT EXTENSION MOVES FIRST FINITENESS PROPERTY AND A TOY FORM OF THE SECOND SECOND FINITENESS PROPERTY FOR SIMPLE 3-MANIFOLDS JACO–SHALEN–JOHANNSON DECOMPOSITION IMPROVING ISOTOPY THAT SEPARATES SURFACES DOES M 3 CONTAIN ESSENTIAL TORI AND ANNULI? DI?ERENT TYPES OF ESSENTIAL TORI AND ANNULI JSJ-DECOMPOSITION EXISTS AND IS UNIQUE SEIFERT AND I-BUNDLE CHAMBERS THIRD FINITENESS PROPERTY EXTENSION MOVES DESCRIPTION OF GENERAL EXTENSION MOVES STRUCTURE OF CHAMBERS SPECIAL EXTENSION MOVES: EASY CASE DI?CULT CASE RECOGNITION OF SIMPLE STALLINGS MANIFOLDS WITH PERIODIC MONODROMY RECOGNITION OF SIMPLE STALLINGS MANIFOLDS WITH NONPERIODIC MONODROMY RECOGNITION OF QUASI-STALLINGS MANIFOLDS SUBDIVISION OF SOLID TORI PROOF OF THE RECOGNITION THEOREM 3-MANIFOLD RECOGNIZER COMPUTER PRESENTATION OF 3-MANIFOLDS CELL COMPLEXES 3-MANIFOLDS AS THICKENED SPINES SIMPLIFYING MANIFOLDS AND SPINES COORDINATE SYSTEMS ON TORI REDUCTION OF CELL STRUCTURES COLLAPSES SURGERIES DISC REPLACEMENT MOVES LABELED MOLECULES WHAT IS A LABELED MOLECULE? CREATING A LABELED MOLECULE ASSEMBLING SEIFERT ATOMS TABULATION COMMENTS ON THE TABLE HYPERBOLIC MANIFOLDS UP TO COMPLEXITY 12 WHY THE TABLE CONTAINS NO DUPLICATES? OTHER APPLICATIONS OF THE 3-MANIFOLD RECOGNIZER ENUMERATION OF HEEGAARD DIAGRAMS OF GENUS 2 3-MANIFOLDS REPRESENTED BY CRYSTALLIZATIONS WITH ?32 VERTICES CLASSI?CATION OF CRYSTALLIZATIONS OF GENUS 2 RECOGNITION OF KNOTS AND UNKNOTS TWO-STEP ENUMERATION OF 3-MANIFOLDS RELATIVE SPINES AND RELATIVE COMPLEXITY ASSEMBLING MODI?ED ENUMERATION OF MANIFOLDS AND SPINES THE TURAEV–VIRO INVARIANTS THE CONSTRUCTION TURAEV–VIRO TYPE INVARIANTS OF ORDER R ?3 CONSTRUCTION AND PROPERTIES OF THE ?-INVARIANT TURAEV–VIRO INVARIANTS OF ORDER R ?3 COMPUTING TURAEV–VIRO INVARIANTS MORE ON ?-INVARIANT 3-MANIFOLDS HAVING THE SAME INVARIANTS OF TURAEV–VIRO TYPE