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Homotopy sphere

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The resolution of the smooth Poincaré conjecture in dimensions 5 and larger implies that homotopy spheres in those dimensions are precisely
71: 159: 292: 261: 123: 287: 297: 254: 128: 95: 56: 177: 20: 165: 155: 99: 91: 118: 64: 238: 52: 281: 106: 87: 203: 79: 109:. It is open whether non-trivial smooth homotopy spheres exist in dimension 4. 24: 169: 226: 208: 234: 40: 36: 149: 48: 242: 63:-sphere, and so every homotopy sphere is necessarily a 94:in dimension 4, and for dimension 3 (the original 262: 8: 182:: CS1 maint: multiple names: authors list ( 269: 255: 140: 175: 7: 223: 221: 90:in dimensions five and higher, by 14: 225: 78:-dimensional homotopy sphere is 72:generalized PoincarĂ© conjecture 1: 148:A., Kosinski, Antoni (1993). 16:Concept in algebraic topology 241:. You can help Knowledge by 314: 220: 124:Homotopy groups of spheres 86:-sphere; it was solved by 51:. It thus has the same 151:Differential manifolds 202:Hedegaard, Rasmus. 129:PoincarĂ© conjecture 96:PoincarĂ© conjecture 41:homotopy equivalent 293:Topological spaces 154:. Academic Press. 21:algebraic topology 250: 249: 204:"Homotopy sphere" 305: 271: 264: 257: 235:topology-related 229: 222: 214: 213: 188: 187: 181: 173: 145: 100:Grigori Perelman 92:Michael Freedman 70:The topological 313: 312: 308: 307: 306: 304: 303: 302: 288:Homotopy theory 278: 277: 276: 275: 218: 201: 200: 197: 192: 191: 174: 162: 147: 146: 142: 137: 119:Homology sphere 115: 65:homology sphere 53:homotopy groups 29:homotopy sphere 17: 12: 11: 5: 311: 309: 301: 300: 298:Topology stubs 295: 290: 280: 279: 274: 273: 266: 259: 251: 248: 247: 230: 216: 215: 196: 195:External links 193: 190: 189: 160: 139: 138: 136: 133: 132: 131: 126: 121: 114: 111: 107:exotic spheres 59:groups as the 23:, a branch of 15: 13: 10: 9: 6: 4: 3: 2: 310: 299: 296: 294: 291: 289: 286: 285: 283: 272: 267: 265: 260: 258: 253: 252: 246: 244: 240: 237:article is a 236: 231: 228: 224: 219: 211: 210: 205: 199: 198: 194: 185: 179: 171: 167: 163: 161:0-12-421850-4 157: 153: 152: 144: 141: 134: 130: 127: 125: 122: 120: 117: 116: 112: 110: 108: 103: 101: 97: 93: 89: 88:Stephen Smale 85: 81: 77: 73: 68: 66: 62: 58: 55:and the same 54: 50: 46: 42: 38: 34: 30: 26: 22: 243:expanding it 232: 217: 207: 150: 143: 104: 83: 80:homeomorphic 75: 74:is that any 69: 60: 44: 32: 28: 18: 25:mathematics 282:Categories 135:References 209:MathWorld 178:cite book 170:875287946 102:in 2005. 113:See also 57:homology 39:that is 37:manifold 82:to the 43:to the 168:  158:  49:sphere 31:is an 233:This 98:) by 239:stub 184:link 166:OCLC 156:ISBN 27:, a 19:In 284:: 206:. 180:}} 176:{{ 164:. 67:. 270:e 263:t 256:v 245:. 212:. 186:) 172:. 84:n 76:n 61:n 47:- 45:n 35:- 33:n

Index

algebraic topology
mathematics
manifold
homotopy equivalent
sphere
homotopy groups
homology
homology sphere
generalized Poincaré conjecture
homeomorphic
Stephen Smale
Michael Freedman
Poincaré conjecture
Grigori Perelman
exotic spheres
Homology sphere
Homotopy groups of spheres
Poincaré conjecture
Differential manifolds
ISBN
0-12-421850-4
OCLC
875287946
cite book
link
"Homotopy sphere"
MathWorld
Stub icon
topology-related
stub

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