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What is the mapping class group of the wedge of circles?

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#algebraic-topology
449
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$f:X\rightarrow S^1$ a continuous map. $X$ a path-connected topological space.

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#general-topology #algebraic-topology
1.3k
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A question about the rotation number of homeomorphisms of the circle

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#algebraic-topology #dynamical-systems #rotations
60
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Is $\textrm{im}(f)$ homeomorphic to the torus less the inner equator?

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#general-topology #algebraic-topology #surfaces
1.2k
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Characteristic classes for quaternionic bundles

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#algebraic-topology #vector-bundles #fiber-bundles
162
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Prove: $U \mapsto \mathrm{Hom}(U, Y)$

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#algebraic-geometry #algebraic-topology #sheaf-theory #ringed-spaces
216
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Characteristic classes not defined on vector bundles

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#algebraic-topology #differential-topology #vector-bundles #characteristic-classes #principal-bundles
120
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A question regarding the set of one-dimensional subspaces being the same as a circle.

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#algebraic-topology
3.1k
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Showing that a homotopy fiber of a fibration is homotopy equivalent to the fiber of the base point.

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#algebraic-topology #homotopy-theory
737
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Are deck transformations homotopic to the identity?

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#algebraic-topology #covering-spaces
123
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Manifolds with non-vanishing vector field and vast homology

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#algebraic-topology #obstruction-theory
824
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lifts of continuous map to covering space

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#algebraic-topology
43
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$H^1(X) = [X,\mathbb{T}]$?

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#algebraic-topology #terminology #examples-counterexamples #homology-cohomology
1k
Views

Can we simultaneously realize arbitrary homotopy groups and arbitrary homology groups?

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#algebraic-topology #homotopy-theory #homology-cohomology
92
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a region homeomorphic with klein bottle

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#general-topology #algebraic-topology

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