List questions from k-theory

Published on 10 May 2026 - 14:05

100

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$a\otimes(-a) = a \otimes (1-a) + a^{-1}\otimes(1-a^{-1})$???

Published on 10 May 2026 - 18:16

314

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Show that $K_2(F)$ is a direct summand of $K_2F(t)$

Published on 10 May 2026 - 18:16

115

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Show that $\pi_{i}(F) \cong \pi_{i +1}(X) $ where $F$ is the homotopy fiber of the inclusion $X \rightarrow X \times X.$

Published on 10 May 2026 - 22:58

79

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Determine with justification, whether $S^2 \times S^4$ is homeomorphic to $\mathbb{C}P^3$.

Published on 13 Apr 2026 - 2:55

169

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Show that the space $Y = S^3 \vee S^6$ has precisely two distinct homotopy classes of comultiplications.

Published on 10 May 2026 - 17:17

77

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What are $\tilde{H_}(K;\mathbb{Z})$ and $\tilde{H^}(K;\mathbb{Z})$?

Published on 09 Apr 2026 - 21:12

2.3k

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Show that the orthogonal group acts transitively on the sphere $S^n.$

Published on 25 Mar 2026 - 12:26

89

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Isomorphism of Projective Modules

Published on 15 Apr 2026 - 3:26

109

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Describe a map $f: S^2 \times S^2 \rightarrow S^4$ such that $f^{*}$ is an isomorphism.

Published on 25 Mar 2026 - 12:28

112

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Calculating the cochain complex of $S^2 \times S^4. $

Published on 13 Apr 2026 - 2:25

39

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Subgroup of $K_0(A)$ generated by projections in $A$, where $A$ is a unital $C^*$-algebra

Published on 14 Apr 2026 - 7:35

59

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Motivation for studying Operator $K_1$

Published on 09 Apr 2026 - 12:08

334

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Problem 22.35 in "Modern Classical Homotopy Theory " by Jeffery Strom on pg.510.

Published on 14 Apr 2026 - 15:14

191

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Verify that $\langle\alpha \cup \beta, u\rangle = \langle\beta, \alpha \cap u\rangle.$

Published on 17 Apr 2026 - 7:07

List Question

$KO_*$ groups of $\mathbb{R}P^\infty$, "Snaiths" theorem for $KO$

$a\otimes(-a) = a \otimes (1-a) + a^{-1}\otimes(1-a^{-1})$???

Show that $K_2(F)$ is a direct summand of $K_2F(t)$

Show that $\pi_{i}(F) \cong \pi_{i +1}(X) $ where $F$ is the homotopy fiber of the inclusion $X \rightarrow X \times X.$

Determine with justification, whether $S^2 \times S^4$ is homeomorphic to $\mathbb{C}P^3$.

Show that the space $Y = S^3 \vee S^6$ has precisely two distinct homotopy classes of comultiplications.

What are $\tilde{H_}(K;\mathbb{Z})$ and $\tilde{H^}(K;\mathbb{Z})$?

Show that the orthogonal group acts transitively on the sphere $S^n.$

Isomorphism of Projective Modules

Describe a map $f: S^2 \times S^2 \rightarrow S^4$ such that $f^{*}$ is an isomorphism.

Calculating the cochain complex of $S^2 \times S^4. $

Subgroup of $K_0(A)$ generated by projections in $A$, where $A$ is a unital $C^*$-algebra

Motivation for studying Operator $K_1$

Problem 22.35 in "Modern Classical Homotopy Theory " by Jeffery Strom on pg.510.

Verify that $\langle\alpha \cup \beta, u\rangle = \langle\beta, \alpha \cap u\rangle.$

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