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001 978-3-540-71807-9
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020 _a9783540718079
_9978-3-540-71807-9
024 7 _a10.1007/978-3-540-71807-9
_2doi
050 4 _aQA613-613.8
050 4 _aQA613.6-613.66
072 7 _aPBMS
_2bicssc
072 7 _aMAT038000
_2bisacsh
072 7 _aPBMS
_2thema
072 7 _aPBPH
_2thema
082 0 4 _a514.34
_223
100 1 _aAkiyoshi, Hirotaka.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 0 _aPunctured Torus Groups and 2-Bridge Knot Groups (I)
_h[electronic resource] /
_cby Hirotaka Akiyoshi, Makoto Sakuma, Masaaki Wada, Yasushi Yamashita.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg,
_c2007.
300 _aXLIII, 256 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1909
505 0 _aJorgensen's picture of quasifuchsian punctured torus groups -- Fricke surfaces and PSL(2, ?)-representations -- Labeled representations and associated complexes -- Chain rule and side parameter -- Special examples -- Reformulation of Main Theorem 1.3.5 and outline of the proof -- Openness -- Closedness -- Algebraic roots and geometric roots.
520 _aThis monograph is Part 1 of a book project intended to give a full account of Jorgensen's theory of punctured torus Kleinian groups and its generalization, with application to knot theory. Although Jorgensen's original work was not published in complete form, it has been a source of inspiration. In particular, it has motivated and guided Thurston's revolutionary study of low-dimensional geometric topology. In this monograph, we give an elementary and self-contained description of Jorgensen's theory with a complete proof. Through various informative illustrations, readers are naturally led to an intuitive, synthetic grasp of the theory, which clarifies how a very simple fuchsian group evolves into complicated Kleinian groups.
650 0 _aCell aggregation
_xMathematics.
650 0 _aFunctions of complex variables.
650 0 _aGroup theory.
650 1 4 _aManifolds and Cell Complexes (incl. Diff.Topology).
_0http://scigraph.springernature.com/things/product-market-codes/M28027
650 2 4 _aFunctions of a Complex Variable.
_0http://scigraph.springernature.com/things/product-market-codes/M12074
650 2 4 _aGroup Theory and Generalizations.
_0http://scigraph.springernature.com/things/product-market-codes/M11078
700 1 _aSakuma, Makoto.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
700 1 _aWada, Masaaki.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
700 1 _aYamashita, Yasushi.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783540837169
776 0 8 _iPrinted edition:
_z9783540718062
830 0 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1909
856 4 0 _uhttps://doi.org/10.1007/978-3-540-71807-9
912 _aZDB-2-SMA
912 _aZDB-2-LNM
999 _c9540
_d9540