Johannson, Klaus.
Topology and Combinatorics of 3-Manifolds [electronic resource] / by Klaus Johannson. - Berlin, Heidelberg : Springer Berlin Heidelberg, 1995. - XVIII, 450 p. online resource. - Lecture Notes in Mathematics, 1599 0075-8434 ; . - Lecture Notes in Mathematics, 1599 .
Handlebodies -- Relative handlebodies -- Generalized one-relator 3-manifolds -- N-relaton 3-manifolds -- The space of heegaard graphs.
This book is a study of combinatorial structures of 3-mani- folds, especially Haken 3-manifolds. Specifically, it is concerned with Heegard graphs in Haken 3-manifolds, i.e., with graphs whose complements have a free fundamental group. These graphs always exist. They fix not only a combinatorial stucture but also a presentation for the fundamental group of the underlying 3-manifold. The starting point of the book is the result that the intersection of Heegard graphs with incompressible surfaces, or hierarchies of such surfaces, is very rigid. A number of finiteness results lead up to a ri- gidity theorem for Heegard graphs. The book is intended for graduate students and researchers in low-dimensional topolo- gy as well as combinatorial theory. It is self-contained and requires only a basic knowledge of the theory of 3-manifolds.
9783540491811
10.1007/BFb0074005 doi
Mathematics.
Group theory.
Algebraic topology.
Cell aggregation--Mathematics.
Mathematics.
Algebraic Topology.
Manifolds and Cell Complexes (incl. Diff.Topology).
Group Theory and Generalizations.
QA612-612.8
514.2
Topology and Combinatorics of 3-Manifolds [electronic resource] / by Klaus Johannson. - Berlin, Heidelberg : Springer Berlin Heidelberg, 1995. - XVIII, 450 p. online resource. - Lecture Notes in Mathematics, 1599 0075-8434 ; . - Lecture Notes in Mathematics, 1599 .
Handlebodies -- Relative handlebodies -- Generalized one-relator 3-manifolds -- N-relaton 3-manifolds -- The space of heegaard graphs.
This book is a study of combinatorial structures of 3-mani- folds, especially Haken 3-manifolds. Specifically, it is concerned with Heegard graphs in Haken 3-manifolds, i.e., with graphs whose complements have a free fundamental group. These graphs always exist. They fix not only a combinatorial stucture but also a presentation for the fundamental group of the underlying 3-manifold. The starting point of the book is the result that the intersection of Heegard graphs with incompressible surfaces, or hierarchies of such surfaces, is very rigid. A number of finiteness results lead up to a ri- gidity theorem for Heegard graphs. The book is intended for graduate students and researchers in low-dimensional topolo- gy as well as combinatorial theory. It is self-contained and requires only a basic knowledge of the theory of 3-manifolds.
9783540491811
10.1007/BFb0074005 doi
Mathematics.
Group theory.
Algebraic topology.
Cell aggregation--Mathematics.
Mathematics.
Algebraic Topology.
Manifolds and Cell Complexes (incl. Diff.Topology).
Group Theory and Generalizations.
QA612-612.8
514.2