By András I. Stipsicz, Robert E. Gompf

ISBN-10: 0821809946

ISBN-13: 9780821809945

The previous twenty years have introduced explosive development in 4-manifold thought. Many books are at the moment showing that process the subject from viewpoints equivalent to gauge idea or algebraic geometry. This quantity, even though, deals an exposition from a topological perspective. It bridges the space to different disciplines and provides classical yet very important topological strategies that experience no longer formerly seemed within the literature. half I of the textual content provides the fundamentals of the speculation on the second-year graduate point and provides an summary of present learn. half II is dedicated to an exposition of Kirby calculus, or handlebody conception on 4-manifolds. it's either basic and complete. half III bargains extensive a huge variety of subject matters from present 4-manifold study. themes contain branched coverings and the geography of advanced surfaces, elliptic and Lefschetz fibrations, $h$-cobordisms, symplectic 4-manifolds, and Stein surfaces. purposes are featured, and there are over three hundred illustrations and diverse workouts with strategies within the booklet.

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Math. Chem. 1993, 14, 175 - 184. Skorobogatov, V. ; Dobrynin, A. A. Metric Analysis of Graphs, Commun. Math. Comput. Chem. (MATCH), 1988, 23, 105-151. ; Balaban, A. T. Iterative Procedure for the Generalized Graph Center in Polycyclic Graphs, J. Chem. Inf. Comput. Sci. 1989, 29, 91-97. Halberstam, F. V. Distance and Path Degree Sequences for Cubic Graphs, Pace University, New York, 1982, A Note on Table of Distance and Path Degree Ssequences for Cubic Graphs, Pace University New York, 1982. Randic, M.

MATCH ), 1997, 35, 145-156. Schultz, H. P. Topological Organic Chemistry. 1. Graph Theory and Topological Indices of Alkanes. J. Chem. Inf. Comput. Sci. 1989, 29, 227-228. Randic, M. Restricted Random Walks on Graphs, Theor. Chim. Acta, 1995, 92, 97-106. Diudea, M. ; Randic, M. Matrix Operator, W(M1,M2,M3) and Schultz-Type Numbers, J. Chem. Inf. Comput. Sci. 1997, 37, 1095-1100. Diudea, M. V. Novel Schultz Analogue Indices, Commun. Math. Comput. Chem. (MATCH ), 1995, 32, 85-103. Diudea, M. ; Pop, C.

65) where ecci is the eccentricity of i. 19 . 23. 19. 24. 18 . 18 ) = 108 4 8 0 0 0 24 8 0 M. V. Diudea, I. Gutman and L. 68) where d(G) is the diameter of the graph. The dimensions of such a matrix are Nx (d(G)+1). 18 . Some properties of LM matrices are given below : (1) The sum of entries in any row equals the sum on the column j = 0 and equals the globa l pro perty M (G). 70) The above relation is valid for any graph, excepting the multigraphs. It represents the essence of the eWM algorithm (see Sect.

### 4-Manifolds and Kirby Calculus (Graduate Studies in Mathematics, Volume 20) by András I. Stipsicz, Robert E. Gompf

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