essential manifold
compact manifold M whose fundamental class [M] defines a nonzero element under the natural homomorphism Hₙ(M) → Hₙ(K(π₁(M),1))
Facts
5 properties- Subclass of
- closed manifold[2]
- Defining formula
- \begin{aligned}&\phi\colon\operatorname H_n(M)\to\operatorname H_n(K(\pi_1(M),1)) \\ &\phi([M]) \ne 0 \end{aligned}[3]
- Discoverer or inventor
- Mikhail Gromov[1]
- Imported from
- wholeness_audit_2026-05-02
- Maintained by WikiProject
- WikiProject Mathematics[4]
🏷️ Also known as
en essential manifold
ru Существенное многообразие
uk Істотний многовид
🔖 Identifiers · 2
- Freebase ID
- /m/04gllhm
- Microsoft Academic ID (discontinued)
- 2779558417
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