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Bers slice

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A Maskit slice is similar to a Bers slice, except that the group is no longer quasi-Fuchsian, and instead of fixing a point in Teichmüller space one fixes a point in the boundary of Teichmüller space.
237: 154: 122: 265: 55:, the limit set is a Jordan curve whose complement has two components. The quotient of each of these components by the groups is a 75: 63:. A Bers slice is a subset of the moduli space of quasi-Fuchsian groups for which one of the two components of this map is a 59:, so we get a map from marked quasi-Fuchsian groups to pairs of Riemann surfaces, and hence to a product of two copies of 229: 70:
The Bers slice gives an embedding of Teichmüller space into the moduli space of quasi-Fuchsian groups, called the
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is a fractal in the Maskit slice separating discrete groups from more chaotic groups.
289: 219: 260: 145:, Grundlehren der Mathematischen Wissenschaften , vol. 287, Berlin, New York: 40: 140: 108: 32: 223: 204: 171:
Minsky, Yair N. (1999), "The classification of punctured-torus groups",
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to a single point in its copy of Teichmüller space.
110:Teichmüller theory and quadratic differentials 8: 222:; Series, Caroline; Wright, David (2002), 186: 7: 74:, and the closure of its image is a 39:, are certain slices through the 14: 78:of Teichmüller space called the 107:Gardiner, Frederick P. (1987), 281:Bers slice for hexagonal torus 19:In the mathematical theory of 1: 276:Bers slice for square torus 312: 266:Pictures of Maskit slices 230:Cambridge University Press 139:Maskit, Bernard (1988), 261:Pictures of Bers slices 174:Annals of Mathematics 115:John Wiley & Sons 80:Bers compactification 53:quasi-Fuchsian group 43:of Kleinian groups. 16:Mathematics concept 239:978-0-521-35253-6 177:, Second Series, 156:978-3-540-17746-3 124:978-0-471-84539-3 65:constant function 61:Teichmüller space 303: 250: 215: 190: 167: 135: 76:compactification 311: 310: 306: 305: 304: 302: 301: 300: 296:Kleinian groups 286: 285: 257: 240: 218: 170: 157: 147:Springer-Verlag 142:Kleinian groups 138: 125: 106: 103: 95:Maskit boundary 88: 57:Riemann surface 49: 21:Kleinian groups 17: 12: 11: 5: 309: 307: 299: 298: 288: 287: 284: 283: 278: 273: 268: 263: 256: 255:External links 253: 252: 251: 238: 225:Indra's pearls 220:Mumford, David 216: 197:10.2307/120976 181:(2): 559–626, 168: 155: 136: 123: 102: 99: 87: 84: 72:Bers embedding 48: 45: 37:Bernard Maskit 31:, named after 15: 13: 10: 9: 6: 4: 3: 2: 308: 297: 294: 293: 291: 282: 279: 277: 274: 272: 269: 267: 264: 262: 259: 258: 254: 249: 245: 241: 235: 231: 227: 226: 221: 217: 214: 210: 206: 202: 198: 194: 189: 184: 180: 176: 175: 169: 166: 162: 158: 152: 148: 144: 143: 137: 134: 130: 126: 120: 116: 112: 111: 105: 104: 100: 98: 96: 91: 86:Maskit slices 85: 83: 81: 77: 73: 68: 66: 62: 58: 54: 46: 44: 42: 38: 34: 30: 29:Maskit slices 26: 22: 271:Maskit slice 224: 188:math/9807001 178: 172: 141: 109: 94: 92: 89: 79: 71: 69: 50: 41:moduli space 28: 24: 18: 47:Bers slices 33:Lipman Bers 25:Bers slices 101:References 205:0003-486X 290:Category 248:1913879 213:1689341 165:0959135 133:0903027 246:  236:  211:  203:  163:  153:  131:  121:  51:For a 183:arXiv 27:and 234:ISBN 201:ISSN 151:ISBN 119:ISBN 93:The 35:and 193:doi 179:149 23:, 292:: 244:MR 242:, 232:, 228:, 209:MR 207:, 199:, 191:, 161:MR 159:, 149:, 129:MR 127:, 117:, 82:. 195:: 185::

Index

Kleinian groups
Lipman Bers
Bernard Maskit
moduli space
quasi-Fuchsian group
Riemann surface
Teichmüller space
constant function
compactification
Teichmüller theory and quadratic differentials
John Wiley & Sons
ISBN
978-0-471-84539-3
MR
0903027
Kleinian groups
Springer-Verlag
ISBN
978-3-540-17746-3
MR
0959135
Annals of Mathematics
arXiv
math/9807001
doi
10.2307/120976
ISSN
0003-486X
MR
1689341

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