0 many and of several different types:
1 a pipe or closed space in a machine that has several openings, allowing liquids and gases to enter and leave
2 many and of different types:
Our organization’s problems are manifold – too few members, too little money, and poor management.
Cycles for the dynamical study of foliated manifolds and complex manifolds.
Families of invariant manifolds corresponding to non-zero characteristics exponents.
Here objects are compact oriented manifolds (boundaries), and morphisms are oriented bordisms (space-times).
All known manifolds with engaging actions of higher rank lattices have an arithmetic fundamental group.
We want also to associate manifolds with boundary to graphs with boundary.
One often considers oriented bordisms, which are oriented manifolds with boundary.
The statement of (2.9) only relies on the topological concepts of orientation and boundaries of manifolds.
Similar definitions hold for functions taking values in manifolds.
