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24 lines
585 B
Markdown
24 lines
585 B
Markdown
# Math4202 Topology II (Lecture 1)
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## Topology of manifolds
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### Fundamental groups
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Use fundamental group as invariant for topological spaces up to homeomorphism (exists bijective and continuous map with continuous inverse) / homotopy equivalence.
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Classifying two dimensional surfaces.
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- Sphere
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- Torus
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- $\mathbb{R}P^2$
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## Quotient spaces
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Let $X$ be a topological space and $f:X\to Y$ is a
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1. continuous
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2. surjective map.
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3. With the property that $U\subset Y$ is open if and only if $f^{-1}(U)$ is open in $X$.
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Then we say $f$ is a quotient map and $Y$ is a quotient space.
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