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Kervaire manifold

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Kervaire, Michel (1960), "A manifold which does not admit any differentiable structure",
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to the result. In 10 dimensions this gives a piecewise-linear manifold with no
112: 258: 194: 274: 118: 76: 33: 139: 91: 55: 294: 8: 301: 287: 117: 75: 38: 32: 104: 7: 255: 253: 14: 182:Commentarii Mathematici Helvetici 257: 134: 119: 1: 273:. You can help Knowledge by 330:Differential geometry stubs 242:Encyclopedia of Mathematics 224:Encyclopedia of Mathematics 107:) by plumbing together the 346: 252: 65:piecewise-linear manifold 235:Shtan'ko, M.A. (2001) , 217:Shtan'ko, M.A. (2001) , 56:{\displaystyle K^{4n+2}} 269:-related article is a 141: 140:{\displaystyle (2n+1)} 93: 57: 320:Differential topology 267:differential geometry 142: 94: 58: 22:differential topology 237:"Dendritic manifold" 219:"Kervaire invariant" 149:, and then gluing a 116: 92:{\displaystyle 4n+2} 74: 31: 101:Michel Kervaire 195:10.1007/BF02565940 137: 89: 53: 20:, specifically in 282: 281: 26:Kervaire manifold 337: 303: 296: 289: 261: 254: 249: 231: 213: 155:smooth structure 146: 144: 143: 138: 98: 96: 95: 90: 62: 60: 59: 54: 52: 51: 345: 344: 340: 339: 338: 336: 335: 334: 310: 309: 308: 307: 234: 216: 178: 175: 163: 114: 113: 109:tangent bundles 99:constructed by 72: 71: 34: 29: 28: 12: 11: 5: 343: 341: 333: 332: 327: 322: 312: 311: 306: 305: 298: 291: 283: 280: 279: 262: 251: 250: 232: 214: 174: 171: 170: 169: 162: 159: 136: 133: 130: 127: 124: 121: 88: 85: 82: 79: 50: 47: 44: 41: 37: 13: 10: 9: 6: 4: 3: 2: 342: 331: 328: 326: 323: 321: 318: 317: 315: 304: 299: 297: 292: 290: 285: 284: 278: 276: 272: 268: 263: 260: 256: 248: 244: 243: 238: 233: 230: 226: 225: 220: 215: 212: 208: 204: 200: 196: 192: 188: 184: 183: 177: 176: 172: 168: 167:Exotic sphere 165: 164: 160: 158: 156: 152: 148: 131: 128: 125: 122: 110: 106: 102: 86: 83: 80: 77: 70: 66: 48: 45: 42: 39: 35: 27: 23: 19: 275:expanding it 264: 240: 222: 186: 180: 25: 15: 189:: 257–270, 18:mathematics 314:Categories 173:References 325:Manifolds 247:EMS Press 229:EMS Press 211:120977898 69:dimension 161:See also 147:-spheres 203:0139172 111:of two 103: ( 209:  201:  265:This 207:S2CID 63:is a 271:stub 151:ball 105:1960 24:, a 191:doi 67:of 16:In 316:: 245:, 239:, 227:, 221:, 205:, 199:MR 197:, 187:34 185:, 157:. 302:e 295:t 288:v 277:. 193:: 135:) 132:1 129:+ 126:n 123:2 120:( 87:2 84:+ 81:n 78:4 49:2 46:+ 43:n 40:4 36:K

Index

mathematics
differential topology
piecewise-linear manifold
dimension
Michel Kervaire
1960
tangent bundles
( 2 n + 1 ) {\displaystyle (2n+1)} -spheres
ball
smooth structure
Exotic sphere
Commentarii Mathematici Helvetici
doi
10.1007/BF02565940
MR
0139172
S2CID
120977898
"Kervaire invariant"
Encyclopedia of Mathematics
EMS Press
"Dendritic manifold"
Encyclopedia of Mathematics
EMS Press
Stub icon
differential geometry
stub
expanding it
v
t

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