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1.

図書
図書
1. Topological polymer chemistry : concepts and practices (: hbk)
Yasuyuki Tezuka, Tetsuo Deguchi, editors
出版情報: Singapore : Springer Nature Singapore, c2022  xi, 436 p. ; 25 cm
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2.

図書
図書
2. General topology (us ; gw)
Jacques Dixmier ; [translated by Sterling K. Berberian]
出版情報: New York : Springer-Verlag, c1984  x, 140 p. ; 25 cm
シリーズ名: Undergraduate texts in mathematics
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3.

図書
図書
3. On topologies and boundaries in potential theory (: Germany ; : U.S.)
Marcel Brelot
出版情報: Berlin ; New York : Springer-Verlag, 1971  vi, 176 p ; 26 cm
シリーズ名: Lecture notes in mathematics ; 175
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4.

図書
図書
4. The Lefschetz fixed point theorem
Robert F. Brown
出版情報: Glenview, Ill. : Scott, Foresman, c1971  vi, 186 p. ; 24 cm
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5.

図書
図書
5. Seifert and Threlfall : a textbook of topology . Seifert : topology of 3-dimensional fibered spaces
H. Seifert and W. Threlfall ; translated by Michael A. Goldman . H. Seifert ; translated by Wolfgang Heil ; edited by Joan S. Birman and Julian Eisner
出版情報: New York : Academic Press, 1980  xvi, 437 p. ; 24 cm
シリーズ名: Pure and applied mathematics ; 89
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6.

図書
図書
6. Topological graph theory
Jonathan L. Gross, Thomas W. Tucker
出版情報: New York : Wiley, c1987  xv, 351 p. ; 24 cm
シリーズ名: Wiley interscience series in discrete mathematics and optimization
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目次情報: 続きを見る
Introduction / 1.：
Representation of graphs / 1.1.：
Drawings / 1.1.1.：
Incidence matrix / 1.1.2.：
Euler's theorem on valence sum / 1.1.3.：
Adjacency matrix / 1.1.4.：
Directions / 1.1.5.：
Graphs, maps, isomorphisms / 1.1.6.：
Automorphisms / 1.1.7.：
Exercises / 1.1.8.：
Some important classes of graphs / 1.2.：
Walks, paths, and cycles; connectedness / 1.2.1.：
Trees / 1.2.2.：
Complete graphs / 1.2.3.：
Cayley graphs / 1.2.4.：
Bipartite graphs / 1.2.5.：
Bouquets of circles / 1.2.6.：
New graphs from old / 1.2.7.：
Subgraphs / 1.3.1.：
Topological representations, subdivisions, graph homeomorphisms / 1.3.2.：
Cartesian products / 1.3.3.：
Edge-complements / 1.3.4.：
Suspensions / 1.3.5.：
Amalgamations / 1.3.6.：
Regular quotients / 1.3.7.：
Regular coverings / 1.3.8.：
Surfaces and imbeddings / 1.3.9.：
Orientable surfaces / 1.4.1.：
Nonorientable surfaces / 1.4.2.：
Imbeddings / 1.4.3.：
Euler's equation for the sphere / 1.4.4.：
Kuratowski's graphs / 1.4.5.：
Genus of surfaces and graphs / 1.4.6.：
The torus / 1.4.7.：
Duality / 1.4.8.：
More graph-theoretic background / 1.4.9.：
Traversability / 1.5.1.：
Factors / 1.5.2.：
Distance, neighborhoods / 1.5.3.：
Graphs colorings and map colorings / 1.5.4.：
Edge operations / 1.5.5.：
Algorithms / 1.5.6.：
Connectivity / 1.5.7.：
Planarity / 1.5.8.：
A nearly complete sketch of the proof / 1.6.1.：
Connectivity and region boundaries / 1.6.2.：
Edge contraction and connectivity / 1.6.3.：
Planarity theorems for 3-connected graphs / 1.6.4.：
Graphs that are not 3-connected / 1.6.5.：
Kuratowski graphs for higher genus / 1.6.6.：
Other planarity criteria / 1.6.8.：
Voltage Graphs and Covering Spaces / 1.6.9.：
Ordinary voltages / 2.1.：
Drawings of voltage graphs / 2.1.1.：
Fibers and the natural projection / 2.1.2.：
The net voltage on a walk / 2.1.3.：
Unique walk lifting / 2.1.4.：
Preimages of cycles / 2.1.5.：
Which graphs are derivable with ordinary voltages? / 2.1.6.：
The natural action of the voltage group / 2.2.1.：
Fixed-point free automorphisms / 2.2.2.：
Cayley graphs revisited / 2.2.3.：
Automorphism groups of graphs / 2.2.4.：
Irregular covering graphs / 2.2.5.：
Schreier graphs / 2.3.1.：
Relative voltages / 2.3.2.：
Combinatorial coverings / 2.3.3.：
Most regular graphs are Schreier graphs / 2.3.4.：
Permutation voltage graphs / 2.3.5.：
Constructing covering spaces with permutations / 2.4.1.：
Preimages of walks and cycles / 2.4.2.：
Which graphs are derivable by permutation voltages? / 2.4.3.：
Identifying relative voltages with permutation voltages / 2.4.4.：
Subgroups of the voltage group / 2.4.5.：
The fundamental semigroup of closed walks / 2.5.1.：
Counting components of ordinary derived graphs / 2.5.2.：
The fundamental group of a graph / 2.5.3.：
Contracting derived graphs onto Cayley graphs / 2.5.4.：
Surfaces and Graph Imbeddings / 2.5.5.：
Surfaces and simplicial complexes / 3.1.：
Geometric simplicial complexes / 3.1.1.：
Abstract simplicial complexes / 3.1.2.：
Triangulations / 3.1.3.：
Cellular imbeddings / 3.1.4.：
Representing surfaces by polygons / 3.1.5.：
Pseudosurfaces and block designs / 3.1.6.：
Orientations / 3.1.7.：
Stars, links, and local properties / 3.1.8.：
Band decompositions and graph imbeddings / 3.1.9.：
Band decomposition for surfaces / 3.2.1.：
Orientability / 3.2.2.：
Rotation systems / 3.2.3.：
Pure rotation systems and orientable surfaces / 3.2.4.：
Drawings of rotation systems / 3.2.5.：
Tracing faces / 3.2.6.：
Which 2-complexes are planar? / 3.2.7.：
The classification of surfaces / 3.2.9.：
Euler characteristic relative to an imbedded graph / 3.3.1.：
Invariance of Euler characteristic / 3.3.2.：
Edge-deletion surgery and edge sliding / 3.3.3.：
Completeness of the set of orientable models / 3.3.4.：
Completeness of the set of nonorientable models / 3.3.5.：
The imbedding distribution of a graph / 3.3.6.：
The absence of gaps in the genus range / 3.4.1.：
The absence of gaps in the crosscap range / 3.4.2.：
A genus-related upper bound on the crosscap number / 3.4.3.：
The genus and crosscap number of the complete graph K[subscript 7] / 3.4.4.：
Some graphs of crosscap number 1 but arbitarily large genus / 3.4.5.：
Maximum genus / 3.4.6.：
Distribution of genus and face sizes / 3.4.7.：
Algorithms and formulas for minimum imbeddings / 3.4.8.：
Rotation-system algorithms / 3.5.1.：
Genus of an amalgamation / 3.5.2.：
Crosscap number of an amalgamation / 3.5.3.：
The White-Pisanski imbedding of a cartesian product / 3.5.4.：
Genus and crosscap number of cartesian products / 3.5.5.：
Imbedded Voltage Graphs and Current Graphs / 3.5.6.：
The derived imbedding / 4.1.：
Lifting rotation systems / 4.1.1.：
Lifting faces / 4.1.2.：
The Kirchhoff Voltage Law / 4.1.3.：
Imbedded permutation voltage graphs / 4.1.4.：
An orientability test for derived surfaces / 4.1.5.：
Branched coverings of surfaces / 4.1.7.：
Riemann surfaces / 4.2.1.：
Extension of the natural covering projection / 4.2.2.：
Which branch coverings come from voltage graphs? / 4.2.3.：
The Riemann-Hurwitz equation / 4.2.4.：
Alexander's theorem / 4.2.5.：
Regular branched coverings and group actions / 4.2.6.：
Groups acting on surfaces / 4.3.1.：
Graph automorphisms and rotation systems / 4.3.2.：
Regular branched coverings and ordinary imbedded voltage graphs / 4.3.3.：
Which regular branched coverings come from voltage graphs? / 4.3.4.：
Applications to group actions on the surface S[subscript 2] / 4.3.5.：
Current graphs / 4.3.6.：
Ringel's generating rows for Heffter's schemes / 4.4.1.：
Gustin's combinatorial current graphs / 4.4.2.：
Orientable topological current graphs / 4.4.3.：
Faces of the derived graph / 4.4.4.：
Nonorientable current graphs / 4.4.5.：
Voltage-current duality / 4.4.6.：
Dual directions / 4.5.1.：
The voltage graph dual to a current graph / 4.5.2.：
The dual derived graph / 4.5.3.：
The genus of the complete bipartite graph K[subscript m, n] / 4.5.4.：
Map Colorings / 4.5.5.：
The Heawood upper bound / 5.1.：
Average valence / 5.1.1.：
Chromatically critical graphs / 5.1.2.：
The five-color theorem / 5.1.3.：
The complete-graph imbedding problem / 5.1.4.：
Triangulations of surfaces by complete graphs / 5.1.5.：
Quotients of complete-graph imbeddings and some variations / 5.1.6.：
A base imbedding for orientable case 7 / 5.2.1.：
Using a coil to assign voltages / 5.2.2.：
A current-graph perspective on case 7 / 5.2.3.：
Orientable case 4: doubling 1-factors / 5.2.4.：
About orientable cases 3 and 0 / 5.2.5.：
The regular nonorientable cases / 5.2.6.：
Some additional tactics / 5.3.1.：
Nonorientable cases 3 and 7 / 5.3.2.：
Nonorientable case 0 / 5.3.4.：
Nonorientable case 4 / 5.3.5.：
About nonorientable cases 1, 6, 9, and 10 / 5.3.6.：
Additional adjacencies for irregular cases / 5.3.7.：
Orientable case 5 / 5.4.1.：
Orientable case 10 / 5.4.2.：
About the other orientable cases / 5.4.3.：
Nonorientable case 5 / 5.4.4.：
About nonorientable cases 11, 8, and 2 / 5.4.5.：
The Genus of a Group / 5.4.6.：
The genus of abelian groups / 6.1.：
Recovering a Cayley graph from any of its quotients / 6.1.1.：
A lower bound for the genus of most abelian groups / 6.1.2.：
Constructing quadrilateral imbeddings for most abelian groups / 6.1.3.：
The symmetric genus / 6.1.4.：
Rotation systems and symmetry / 6.2.1.：
Reflections / 6.2.2.：
Quotient group actions on quotient surfaces / 6.2.3.：
Alternative Cayley graphs revisited / 6.2.4.：
Group actions and imbeddings / 6.2.5.：
Are genus and symmetric genus the same? / 6.2.6.：
Euclidean space groups and the torus / 6.2.7.：
Triangle groups / 6.2.8.：
Groups of small symmetric genus / 6.2.9.：
The Riemann-Hurwitz equation revisited / 6.3.1.：
Strong symmetric genus 0 / 6.3.2.：
Symmetric genus 1 / 6.3.3.：
The geometry and algebra of groups of symmetric genus 1 / 6.3.4.：
Hurwitz's theorem / 6.3.5.：
Groups of small genus / 6.3.6.：
An example / 6.4.1.：
A face-size inequality / 6.4.2.：
Statement of main theorem / 6.4.3.：
Proof of Theorem 6.4.2: valence d = 4 / 6.4.4.：
Proof of Theorem 6.4.2: valence d = 3 / 6.4.5.：
Remarks about Theorem 6.4.2 / 6.4.6.：
References / 6.4.7.：
Bibliography
Supplementary Bibliography
Table of Notations
Subject Index
Introduction / 1.：
Representation of graphs / 1.1.：
Drawings / 1.1.1.：
7.

図書
図書
7. Topology and geometry for physicists (: pbk)
Charles Nash, Siddhartha Sen
出版情報: London ; Tokyo : Academic Press, 1983  x, 311 p. ; 24 cm
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目次情報: 続きを見る
Preface
Basic Notions of Topology and the Value of Topological Reasoning
Differential Geometry
Manifolds and Differential Forms
The Fundamental Group
The Homology Groups
The Higher Homotopy Groups
Cohomology and De Rham Cohomology
Fibre Bundles and Further Differential Geometry
Morse Theory
Defects, Textures, and Homotopy Theory
Yang-Mills Theories
Instantons and Monopoles
Subject Index
Preface
Basic Notions of Topology and the Value of Topological Reasoning
Differential Geometry
8.

図書
図書
8. Real analysis with point-set topology
Donald L. Stancl, Mildred L. Stancl
出版情報: New York : M. Dekker, c1987  x, 287 p. ; 24 cm
シリーズ名: Monographs and textbooks in pure and applied mathematics ; 113
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9.

図書
図書
9. Topology. New ed., rev. and augm (v. 1 ; v. 2)
K. Kuratowski ; translated from French by J. Jaworowski
出版情報: New York : Academic Press, 1966-1968  2 v. ; 24 cm
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10.

図書
図書
10. Fundamental concepts of topology
Peter V. O'Neil
出版情報: New York : Gordon and Breach Science Publishers, c1972  xv, 320 p ; 24 cm
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