| 1. | Next, any map on the M�bius group is homotopic to the identity.
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| 2. | From this point of view, is a homotopic.
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| 3. | Requiring that two embeddings be isotopic is a stronger requirement than that they be homotopic.
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| 4. | In particular we find that vector bundles inducing homotopic maps to the Grassmannian are isomorphic.
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| 5. | The relation of being homotopic is an equivalence relation on paths in a topological space.
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| 6. | By our assumption, and are piecewise smooth homotopic, there are the piecewise smooth homogony
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| 7. | This means that we can consider homotopic equivalence class of paths to have different weighting factors.
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| 8. | But the definition of homotopic relies on a notion of continuity, and hence a topology.
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| 9. | Isotopy invariance of the linking number is automatically obtained as the degree is invariant under homotopic maps.
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| 10. | Merker, for instance, argues that the homotopic connectivity of sensory pathways does the necessary work.
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