Notes for Rigidity Seminar Gromov’s Proof of Mostow Rigidity Theorem
نویسنده
چکیده
we introduce a homological invariant of a manifold known as Gromov’s norm. Gromov’s norm of hyperbolic manifolds will be seen to be proportional to the volume of the manifold. The first striking consequence of this result is that the volume of a hyperbolic manifold is a topological invariant. Intuitively, Gromov’s norm measures the efficiency with which multiples of a homology class can be represented by simplices. A complicated homology class needs many simplices. Definition 2.1 (Gromov Norm). Consider the homomorphism i∗ : H2(S, ∂S;Z)→ H2(S, ∂S;R)
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