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Results tagged with gt.geometric-topology
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user 172285
Topology of cell complexes and manifolds, classification of manifolds (e.g. smoothing, surgery), low dimensional topology (e.g. knot theory, invariants of 4-manifolds), embedding theory, combinatorial and PL topology, geometric group theory, infinite dimensional topology (e.g. Hilbert cube manifolds, theory of retracts).
2
votes
1
answer
272
views
Lifting of a proper map in the cover is a proper map
Let $M$ be an orientable surface without boundary$($I am not assuming $M$ is compact, it can be non-compact$)$. Let $\Phi: M\to M$ be a proper homotopy-equivalnce$($A proper homotopy-equivalence can b …
- 265
8
votes
2
answers
257
views
Degree one self-map of $\Bbb R^2\big\backslash \big\{(n,0):n\in \Bbb Z\big\}$ not homotopic ...
Consider the surface $\Sigma=\Bbb R^2\big\backslash \big\{(n,0):n\in \Bbb Z\big\}$. Does there exist a proper
map $f\colon \Sigma\to \Sigma$ of degree $1$ and not homotopic to
any self-homotopy equiv …
- 265
1
vote
0
answers
163
views
Uniqueness of collar neighborhoods for non-compact boundary case in smooth setting
Let $M$ be a smooth manifold and let $f_0, f_1 \colon [0, 1] \times
\partial M \to M$ be two smooth embeddings that are the identity map
on $\partial M \times\{0\} = \partial M$ . If $\partial M$ is …
- 265