Handle body

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In mathematics , handle bodies are 3-dimensional structures, the edges of which are surfaces .

definition

A full sphere with 3 disjoint handles.

The handle body of the sex is obtained by attaching disjoint handles to a 3-dimensional full sphere .

In formulas: Let a solid sphere, let injective continuous mappings with disjoint images, then we define the handle body as the quotient of

under the equivalence relation for .

is an orientable 3-dimensional manifold with a border , its border is a surface of the gender . The full ball is referred to as the handle body by gender .

Compression body

A more general term, which is mainly used in the theory of 3-manifolds with a boundary , is the term of the compression body .

A compression body is created from a product , for a closed surface , by gluing 2 handles along it . One designates and .

Handle body is obtained for , in this case it is .

literature

  • Bonahon : Geometric structures on 3-manifolds. Handbook of geometric topology, 93-164, North-Holland, Amsterdam, 2002.
  • Bonahon: Cobordism of automorphisms of surfaces. Ann. Sci. École Norm. Sup. (4) 16 (1983) no. 2, 237-270. pdf
  • Lackenby, Purcell: Geodesics and compression bodies pdf
  • Oertel: Automorphisms of three-dimensional handlebodies. Topology 41 (2002), no. 2, 363-410. pdf