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Deficiencies of
immersions
Uri Srebro |
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Vol. 113 (1984), No. 2, 493–496
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Abstract |
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Let X and Y be manifolds of the same dimension n ≥ 2 and let f : X → Y be an immersion with p = sup{n(y) : y ∈ Y } < ∞ where n(y) = cardinality f−1(y). If Y is compact and X is not, then n(y) < p for some y ∈ Y , see §2. If Y is compact and simply connected and p ≥ 2, then Y contains a compact set E such that Y − E is not simply connected and n(y) ≤ p − 2 for all y ∈ E, see §5. |
Mathematical Subject Classification 2000
Primary: 57R40
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Milestones
Received: 21 May 1982
Published: 1 August 1984
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Authors |
| Uri Srebro | |
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