000			03583nam a22004815i 4500
001			978-1-4614-6971-1
003			DE-He213
005			20140220082827.0
007			cr nn 008mamaa
008			130628s2013 xxu| s |||| 0|eng d
020			_a9781461469711 _9978-1-4614-6971-1
024	7		_a10.1007/978-1-4614-6971-1 _2doi
050		4	_aQA166-166.247
072		7	_aPBV _2bicssc
072		7	_aMAT013000 _2bisacsh
082	0	4	_a511.5 _223
100	1		_aEllis-Monaghan, Joanna A. _eauthor.
245	1	0	_aGraphs on Surfaces _h[electronic resource] : _bDualities, Polynomials, and Knots / _cby Joanna A. Ellis-Monaghan, Iain Moffatt.
264		1	_aNew York, NY : _bSpringer New York : _bImprint: Springer, _c2013.
300			_aXI, 139 p. 82 illus., 41 illus. in color. _bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_atext file _bPDF _2rda
490	1		_aSpringerBriefs in Mathematics, _x2191-8198
505	0		_a1. Embedded Graphs -- 2. Generalised Dualities -- 3. Twisted duality, cycle family graphs, and embedded graph equivalence -- 4. Interactions with Graph Polynomials -- 5. Applications to Knot Theory .- References -- Index .
520			_aGraphs on Surfaces: Dualities, Polynomials, and Knots offers an accessible and comprehensive treatment of recent developments on generalized duals of graphs on surfaces, and their applications. The authors  illustrate the interdependency between duality, medial graphs and knots; how this interdependency is reflected in algebraic invariants of graphs and knots; and how it can be exploited to solve problems in graph and knot theory. Taking  a constructive approach, the authors emphasize how generalized duals and related ideas arise by localizing classical constructions, such as geometric duals and Tait graphs, and then removing artificial restrictions in these constructions to obtain full extensions of them to embedded graphs. The authors demonstrate the benefits of these generalizations to embedded graphs in chapters describing their applications to graph polynomials and knots.    Graphs on Surfaces: Dualities, Polynomials, and Knots  also provides a self-contained introduction to graphs on surfaces, generalized duals, topological graph polynomials, and knot polynomials that is accessible both to graph theorists and to knot theorists.  Directed at those with some familiarity with basic graph theory and knot theory, this book is appropriate for graduate students and researchers in either area. Because the area is advancing so rapidly, the authors give a comprehensive overview of the topic and include a robust bibliography, aiming to provide the reader with the necessary foundations to stay abreast of the field. The reader will come away from the text convinced of advantages of considering these higher genus analogues of constructions of plane and abstract graphs, and with a good understanding of how they arise.
650		0	_aMathematics.
650		0	_aTopology.
650		0	_aAlgebraic topology.
650	1	4	_aMathematics.
650	2	4	_aGraph Theory.
650	2	4	_aTopology.
650	2	4	_aAlgebraic Topology.
700	1		_aMoffatt, Iain. _eauthor.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9781461469704
830		0	_aSpringerBriefs in Mathematics, _x2191-8198
856	4	0	_uhttp://dx.doi.org/10.1007/978-1-4614-6971-1
912			_aZDB-2-SMA
999			_c95809 _d95809