%PDF-1.4 % 3 0 obj << /pgfprgb [/Pattern /DeviceRGB] >> endobj 4 0 obj << /S /GoTo /D (section.1) >> endobj 7 0 obj (1. Background and history) endobj 8 0 obj << /S /GoTo /D (subsection.1.1) >> endobj 11 0 obj (1.1. Pontryagin's early work on homotopy groups of spheres) endobj 12 0 obj << /S /GoTo /D (subsection.1.2) >> endobj 15 0 obj (1.2. Our main result) endobj 16 0 obj << /S /GoTo /D (subsection.1.3) >> endobj 19 0 obj (1.3. The manifold formulation) endobj 20 0 obj << /S /GoTo /D (subsection.1.4) >> endobj 23 0 obj (1.4. The unstable formulation) endobj 24 0 obj << /S /GoTo /D (subsection.1.5) >> endobj 27 0 obj (1.5. Questions raised by our theorem) endobj 28 0 obj << /S /GoTo /D (section.2) >> endobj 31 0 obj (2. Our strategy) endobj 32 0 obj << /S /GoTo /D (subsection.2.1) >> endobj 35 0 obj (2.1. Ingredients of the proof) endobj 36 0 obj << /S /GoTo /D (subsection.2.2) >> endobj 39 0 obj (2.2. The spectrum ) endobj 40 0 obj << /S /GoTo /D (subsection.2.3) >> endobj 43 0 obj (2.3. How we construct ) endobj 44 0 obj << /S /GoTo /D (subsection.2.4) >> endobj 47 0 obj (2.4. The norm) endobj 48 0 obj << /S /GoTo /D (subsection.2.5) >> endobj 51 0 obj (2.5. Fixed points and homotopy fixed points) endobj 52 0 obj << /S /GoTo /D (subsection.2.6) >> endobj 55 0 obj (2.6. RO \(G\)-graded homotopy) endobj 56 0 obj << /S /GoTo /D (section.3) >> endobj 59 0 obj (3. The slice filtration) endobj 60 0 obj << /S /GoTo /D (subsection.3.1) >> endobj 63 0 obj (3.1. Postnikov towers) endobj 64 0 obj << /S /GoTo /D (subsection.3.2) >> endobj 67 0 obj (3.2. Slice cells) endobj 68 0 obj << /S /GoTo /D (subsection.3.3) >> endobj 71 0 obj (3.3. The slice tower) endobj 72 0 obj << /S /GoTo /D (subsection.3.4) >> endobj 75 0 obj (3.4. The Slice Theorem) endobj 76 0 obj << /S /GoTo /D (subsection.3.5) >> endobj 79 0 obj (3.5. Refining u*MU\(G\)) endobj 80 0 obj << /S /GoTo /D (subsection.3.6) >> endobj 83 0 obj (3.6. The definition of O) endobj 84 0 obj << /S /GoTo /D (section.4) >> endobj 87 0 obj (4. The Gap Theorem) endobj 88 0 obj << /S /GoTo /D (subsection.4.1) >> endobj 91 0 obj (4.1. Derivation from the Slice Theorem) endobj 92 0 obj << /S /GoTo /D (subsection.4.2) >> endobj 95 0 obj (4.2. An easy calculation) endobj 96 0 obj << /S /GoTo /D (section.5) >> endobj 99 0 obj (5. The Periodicity Theorem) endobj 100 0 obj << /S /GoTo /D (subsection.5.1) >> endobj 103 0 obj (5.1. Geometric fixed points) endobj 104 0 obj << /S /GoTo /D (subsection.5.2) >> endobj 107 0 obj (5.2. Some slice differentials) endobj 108 0 obj << /S /GoTo /D (subsection.5.3) >> endobj 111 0 obj (5.3. Some RO \(G\)-graded calculations) endobj 112 0 obj << /S /GoTo /D (subsection.5.4) >> endobj 115 0 obj (5.4. An even trickier RO \(G\)-graded calculation) endobj 116 0 obj << /S /GoTo /D (subsection.5.5) >> endobj 119 0 obj (5.5. The proof of the Periodicity Theorem) endobj 120 0 obj << /S /GoTo /D (section.6) >> endobj 123 0 obj (6. The Homotopy Fixed Point Theorem) endobj 124 0 obj << /S /GoTo /D (section.7) >> endobj 127 0 obj (7. The Detection Theorem) endobj 128 0 obj << /S /GoTo /D (subsection.7.1) >> endobj 131 0 obj (7.1. j in the Adams-Novikov spectral sequence) endobj 132 0 obj << /S /GoTo /D (subsection.7.2) >> endobj 135 0 obj (7.2. Formal A-modules) endobj 136 0 obj << /S /GoTo /D (subsection.7.3) >> endobj 139 0 obj (7.3. The relation between MU\(C8\) and formal A-modules) endobj 140 0 obj << /S /GoTo /D (subsection.7.4) >> endobj 143 0 obj (7.4. The proof of the Detection Theorem) endobj 144 0 obj << /S /GoTo /D (subsection.7.5) >> endobj 147 0 obj (7.5. The proof of Lemma 2) endobj 148 0 obj << /S /GoTo /D (section.8) >> endobj 151 0 obj (8. The Slice and Reduction theorems) endobj 152 0 obj << /S /GoTo /D (section*.3) >> endobj 155 0 obj (References) endobj 156 0 obj << /S /GoTo /D [157 0 R /Fit ] >> endobj 170 0 obj << /Length 1033 /Filter /FlateDecode >> stream xڅUo8%ĉӖmeKs+}` sNMlČ|Ow?C cxD$ĉR0%j?wMF7 OQw&{ݩw `
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