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15
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How do continuous maps between spaces induce homomorphisms between Cech cohomologies?

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#general-topology #algebraic-topology #homological-algebra
737
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Higher homotopy groups of surface of genus 2, without using universal cover

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#algebraic-topology #higher-homotopy-groups
113
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Existence of an element in $K^0$ group, Koszul complexes

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#differential-geometry #algebraic-topology #vector-bundles #characteristic-classes #topological-k-theory
428
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How are the homology groups of map space related to the "factors"?

Published on
#reference-request #algebraic-topology #homology-cohomology #homotopy-theory
58
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Cyclic covers and "cut-open" curves

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#algebraic-topology #low-dimensional-topology
102
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Is inclusion in a cone an embedding?

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#general-topology #algebraic-topology
343
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Tom Dieck 4.6, Exercise 1, pg 96, Pushout and quotient maps

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#general-topology #algebraic-topology #category-theory
799
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Question on star shaped domains

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#general-topology #algebraic-topology
32
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What is intersection of an $m$-handle and an $n$-manifold in a handle decomposition?

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#general-topology #algebraic-topology
342
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What is the free loop space $\mathcal{L}M$ of a manifold of a manifold $M$ for which the energy functional has no critical points?

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#algebraic-topology #morse-theory #loop-spaces
111
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What is the induced isomorphism of a handle decomposition $X_k=X_{k-1}\cup H^{\lambda_k}$, $X_0=D^m$ given by the long exact Mayer-Vietoris sequence?

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#algebraic-topology #homology-cohomology
237
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Fundamental group of a quotient of a cylinder

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#general-topology #algebraic-topology #fundamental-groups #semidirect-product
55
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a compact set with nonempty convex sections

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#general-topology #algebraic-topology #convex-analysis #convex-geometry
160
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Do long exact Mayer Vietoris sequences decompose into short exact sequences $0\to H_n(A\cap B)\to H_n(A)\oplus H_n(B)\to H_n(X)\to 0$?

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#algebraic-topology #exact-sequence
78
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Image of exact sequence still exact?

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#algebraic-geometry #algebraic-topology #homotopy-theory #fiber-bundles #exact-sequence

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