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Results tagged with manifolds
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user 148161
A manifold is a topological space that locally resembles Euclidean space near each point. More precisely, each point of an n-dimensional manifold has a neighbourhood that is homeomorphic to the Euclidean space of dimension n.
44
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4
answers
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Do rings of smooth functions differ from rings of continuous functions?
Let $M$, $N$ be connected nondiscrete compact smooth manifolds. Can the ring of continuous functions on $M$ be isomorphic to the ring of smooth functions on $N$? …
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7
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Can every finitely presented group be realized as a fundamental group of a compact four-dime...
Every finitely presented group is realized as a fundamental group of a two-dimensional complex (a simple exercise on Van Kampen's theorem). I was told that a two-dimensional complex can be well embedd …
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6
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answers
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Does there exist a manifold with finitely generated homology groups that is not homotopy equ...
I wrote earlier if the finitely generated of the homology groups implies the finitely generated of the fundamental group (noticed in the comments that this is not true), then for 3-manifolds, by Scott's … compact kernel theorem, there are no such manifolds: a three-dimensional manifold admits a smooth structure, then it is triangulable, hence homeomorphic to a CW-complex, and CW-complexes with isomorphic …
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3
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CW-complexes that cannot be homotopically compressed
Due to (3), it is interesting - is it true that every connected n-dimensional CW-complex is homotopy equivalent to a bunch of n-dimensional closed manifolds? … What is the criterion for incompressibility for non-closed manifolds? Are homotopy incompressible spaces closed with respect to a bouquet, product .. …
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