000			03078nam a22004695i 4500
001			978-1-4471-2158-9
003			DE-He213
005			20180115171508.0
007			cr nn 008mamaa
008			111125s2012 xxk| s |||| 0|eng d
020			_a9781447121589 _9978-1-4471-2158-9
024	7		_a10.1007/978-1-4471-2158-9 _2doi
050		4	_aQA241-247.5
072		7	_aPBH _2bicssc
072		7	_aMAT022000 _2bisacsh
082	0	4	_a512.7 _223
100	1		_aMorishita, Masanori. _eauthor.
245	1	0	_aKnots and Primes _h[electronic resource] : _bAn Introduction to Arithmetic Topology / _cby Masanori Morishita.
264		1	_aLondon : _bSpringer London, _c2012.
300			_aXI, 191p. 42 illus. _bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_atext file _bPDF _2rda
490	1		_aUniversitext, _x0172-5939
505	0		_aPreliminaries - Fundamental Groups and Galois Groups -- Knots and Primes, 3-Manifolds and Number Rings -- Linking Numbers and Legendre Symbols -- Decompositions of Knots and Primes -- Homology Groups and Ideal Class Groups I - Genus Theory -- Link Groups and Galois Groups with Restricted Ramification -- Milnor Invariants and Multiple Power Residue Symbols -- Alexander Modules and Iwasawa Modules -- Homology Groups and Ideal Class Groups II - Higher Order Genus Theory -- Homology Groups and Ideal Class Groups III - Asymptotic Formulas -- Torsions and the Iwasawa Main Conjecture -- Moduli Spaces of Representations of Knot and Prime Groups -- Deformations of Hyperbolic Structures and of p-adic Ordinary Modular Forms.
520			_aThis is a foundation for arithmetic topology - a new branch of mathematics which is focused upon the analogy between knot theory and number theory.  Starting with an informative introduction to its origins, namely Gauss, this text provides a background on knots, three manifolds and number fields. Common aspects of both knot theory and number theory, for instance knots in three manifolds versus primes in a number field, are compared throughout the book. These comparisons begin at an elementary level, slowly building up to advanced theories in later chapters. Definitions are carefully formulated and proofs are largely self-contained. When necessary, background information is provided and theory is accompanied  with a number of useful examples and illustrations, making this a useful text for both undergraduates and graduates in the field of knot theory, number theory and geometry.
650		0	_aMathematics.
650		0	_aNumber theory.
650		0	_aTopology.
650	1	4	_aMathematics.
650	2	4	_aNumber Theory.
650	2	4	_aTopology.
650	2	4	_aMathematics, general.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9781447121572
830		0	_aUniversitext, _x0172-5939
856	4	0	_uhttp://dx.doi.org/10.1007/978-1-4471-2158-9
912			_aZDB-2-SMA
999			_c370401 _d370401