List questions from homotopy-theory

Published on 29 Jun 2019 - 6:06

147

Views

Replacing the fibre of a fibration.

Published on 12 Apr 2026 - 21:40

488

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Induction on identity types in HoTT and dependent type theory

Published on 13 Apr 2026 - 16:02

36

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Why if $n\geq1$ and $0\leq i\leq j\leq n$ then $F_n^j\circ F_{n-1}^i=F_n^i\circ F_{n-1}^{j-1}$?

Published on 26 Mar 2026 - 20:41

129

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Poset map and fibration

Published on 11 Apr 2026 - 18:42

364

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If $f,g:(X,A)\to (Y,B)$ are homotopic functions under a homotopy $H:X\times [0,1]\to Y$ then $f_=g_:H_n(X,A)\to H_n(Y,B)$.

Published on 13 Apr 2026 - 22:08

120

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What happens if we remove the point of origin from the moebius band?

Published on 14 Apr 2026 - 0:41

56

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Paths and loops.

Published on 11 Apr 2026 - 10:01

138

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The definition of the product of 2 paths.

Published on 13 Apr 2026 - 21:05

93

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Elaboration of some ideas on identity path.

Published on 11 Apr 2026 - 11:53

148

Views

A space is homotopy equivalent to its Kolmogorov quotient

Published on 12 Apr 2026 - 12:29

47

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Product of any 2 p-based loops is again a p-based loop.

Published on 13 Apr 2026 - 21:23

439

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Proving the existence of identity of the fundamental group of homotopy theory $ \pi ( X,p)$

Published on 25 Mar 2026 - 17:44

420

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How do I prove the existence of inverse of the fundamental group $ \pi ( X)$.

Published on 10 Apr 2026 - 12:53

804

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Is there any analogy between homotopy of spaces and homotopy between maps?

Published on 12 Apr 2026 - 10:50

List Question

Loops of intersection number $\geq 1$ in orientable surface of genus $2$.

Replacing the fibre of a fibration.

Induction on identity types in HoTT and dependent type theory

Why if $n\geq1$ and $0\leq i\leq j\leq n$ then $F_n^j\circ F_{n-1}^i=F_n^i\circ F_{n-1}^{j-1}$?

Poset map and fibration

If $f,g:(X,A)\to (Y,B)$ are homotopic functions under a homotopy $H:X\times [0,1]\to Y$ then $f_=g_:H_n(X,A)\to H_n(Y,B)$.

What happens if we remove the point of origin from the moebius band?

Paths and loops.

The definition of the product of 2 paths.

Elaboration of some ideas on identity path.

A space is homotopy equivalent to its Kolmogorov quotient

Product of any 2 p-based loops is again a p-based loop.

Proving the existence of identity of the fundamental group of homotopy theory $ \pi ( X,p)$

How do I prove the existence of inverse of the fundamental group $ \pi ( X)$.

Is there any analogy between homotopy of spaces and homotopy between maps?

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