Knowledge

Boundary parallel

Source ๐Ÿ“

386: 366: 402: 22: 311: 228: 365: 236: 385: 401: 94: 66: 73: 43: 113: 51: 80: 47: 62: 430: 321: 200: 32: 36: 87: 195: 8: 176: 337: 179: 131: 306:{\displaystyle \pi \colon I\times S^{1}\rightarrow S^{1},\quad (x,z)\mapsto z.} 424: 168: 127: 352: 329: 144: 21: 138: 359:
is not boundary parallel. (Again, the converse is not true.)
347:
is embedded into the annulus so that ฯ€ restricted to
239: 203: 305: 222: 422: 407:An example wherein π is not surjective on 371:An example wherein π is not bijective on 50:. Unsourced material may be challenged and 391:An example wherein π is bijective on 114:Learn how and when to remove this message 320:is embedded into the annulus so that ฯ€ 423: 48:adding citations to reliable sources 15: 13: 230:. Let ฯ€ denote the projection map 14: 442: 400: 384: 364: 343:If, on the other hand, a circle 20: 278: 294: 291: 279: 262: 1: 416: 223:{\displaystyle I\times S^{1}} 189: 7: 379:is ∂-parallel anyway. 336:is boundary parallel. (The 10: 447: 307: 224: 308: 225: 237: 201: 44:improve this article 63:"Boundary parallel" 431:Geometric topology 303: 220: 167:) if there is an 157:boundary parallel 124: 123: 116: 98: 438: 404: 388: 368: 312: 310: 309: 304: 274: 273: 261: 260: 229: 227: 226: 221: 219: 218: 119: 112: 108: 105: 99: 97: 56: 24: 16: 446: 445: 441: 440: 439: 437: 436: 435: 421: 420: 419: 412: 405: 396: 389: 380: 369: 269: 265: 256: 252: 238: 235: 234: 214: 210: 202: 199: 198: 192: 120: 109: 103: 100: 57: 55: 41: 25: 12: 11: 5: 444: 434: 433: 418: 415: 414: 413: 406: 399: 397: 390: 383: 381: 370: 363: 340:is not true.) 314: 313: 302: 299: 296: 293: 290: 287: 284: 281: 277: 272: 268: 264: 259: 255: 251: 248: 245: 242: 217: 213: 209: 206: 191: 188: 151:+ 1)-manifold 122: 121: 28: 26: 19: 9: 6: 4: 3: 2: 443: 432: 429: 428: 426: 410: 403: 398: 394: 387: 382: 378: 374: 367: 362: 361: 360: 358: 354: 350: 346: 341: 339: 335: 331: 327: 323: 319: 300: 297: 288: 285: 282: 275: 270: 266: 257: 253: 249: 246: 243: 240: 233: 232: 231: 215: 211: 207: 204: 197: 194:Consider the 187: 185: 181: 178: 174: 170: 166: 162: 158: 154: 150: 146: 143: 140: 136: 133: 129: 118: 115: 107: 104:December 2009 96: 93: 89: 86: 82: 79: 75: 72: 68: 65: โ€“  64: 60: 59:Find sources: 53: 49: 45: 39: 38: 34: 29:This article 27: 23: 18: 17: 408: 392: 376: 372: 356: 348: 344: 342: 333: 325: 317: 316:If a circle 315: 193: 183: 172: 164: 160: 156: 152: 148: 141: 134: 125: 110: 101: 91: 84: 77: 70: 58: 42:Please help 30: 128:mathematics 417:References 353:surjective 322:restricted 190:An example 165:peripheral 161:โˆ‚-parallel 74:newspapers 330:bijection 295:↦ 263:→ 250:× 244:: 241:π 208:× 180:component 31:does not 425:Category 338:converse 177:boundary 145:embedded 139:manifold 355:, then 351:is not 332:, then 196:annulus 175:onto a 169:isotopy 147:in an ( 88:scholar 52:removed 37:sources 375:, but 132:closed 90:  83:  76:  69:  61:  328:is a 163:, or 95:JSTOR 81:books 159:(or 130:, a 67:news 35:any 33:cite 324:to 182:of 171:of 155:is 126:In 46:by 427:: 186:. 411:. 409:S 395:. 393:S 377:S 373:S 357:S 349:S 345:S 334:S 326:S 318:S 301:. 298:z 292:) 289:z 286:, 283:x 280:( 276:, 271:1 267:S 258:1 254:S 247:I 216:1 212:S 205:I 184:M 173:N 153:M 149:n 142:N 137:- 135:n 117:) 111:( 106:) 102:( 92:ยท 85:ยท 78:ยท 71:ยท 54:. 40:.

Index


cite
sources
improve this article
adding citations to reliable sources
removed
"Boundary parallel"
news
newspapers
books
scholar
JSTOR
Learn how and when to remove this message
mathematics
closed
manifold
embedded
isotopy
boundary
component
annulus
restricted
bijection
converse
surjective
An example wherein ฯ€ is not bijective on S, but S is โˆ‚-parallel anyway.
An example wherein ฯ€ is bijective on S.
An example wherein ฯ€ is not surjective on S.
Category
Geometric topology

Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.

โ†‘