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15
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equivalent characterizations of manifolds such that configuration spaces are homotopy equivalent

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#algebraic-topology #manifolds #homotopy-theory #geometric-topology
268
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Deleting a contractible subspace is the same as deleting a point

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#algebraic-topology #examples-counterexamples #homotopy-theory
120
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isotopy equivalence between manifolds

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#general-topology #algebraic-topology #differential-topology #homotopy-theory #geometric-topology
2.2k
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Prove that the Torus is not homotopy equivalent to $S^1\vee S^1\vee S^2$

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#general-topology #algebraic-topology #homology-cohomology #homotopy-theory
86
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Convergence of continuation scheme for fixed-point via homotopy

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#functional-analysis #optimization #numerical-methods #homotopy-theory #fixed-point-theorems
2.1k
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Showing that $\mathbb S^1$ is a deformation retract of the Mobius strip, rigorously.

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#general-topology #homotopy-theory #quotient-spaces #compact-manifolds #mobius-band
228
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Clarification about the Thom-Pontrjagin construction as explained in Bredon's book

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#algebraic-topology #homotopy-theory #cobordism
2.5k
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Gap between "fibration" and "fiber bundle".

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#homotopy-theory #fiber-bundles #fibration
50
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How stable is the top cell of Lie group?

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#lie-groups #homotopy-theory #stable-homotopy-theory
907
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If the product of two homotopy equivalences is a homotopy equivalence are the factors homotopy equivalences?

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#general-topology #algebraic-topology #homotopy-theory
126
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Another clarification about Thom-Pontrjagin construction

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#algebraic-topology #homotopy-theory #cobordism
555
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Does symplectic K-theory $KSp$ have products?

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#homotopy-theory #quaternions #topological-k-theory #stable-homotopy-theory
1k
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$S^n$ is not a retract of the disk $D^{n+1}$ and Brouwer's Fixed Point Theorem.

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#differential-geometry #differential-topology #homotopy-theory
625
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Proving that the tangent vector of a simple closed curve rotates by $ 2 \pi$

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#differential-geometry #algebraic-topology #homotopy-theory #covering-spaces
436
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Choosing projective replacement to be functorial

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#category-theory #homological-algebra #homotopy-theory #abelian-categories #derived-functors

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