Question

If the canonically fitted unit circle $S^1 \subset S^n$ is removed from $S^n$, prove that the remaining space is homotopically equivalent to $S^{n-2}$. *Remember that $S^n := \{x \in \mathbb{R}^{n+1} : ||x|| = 1\}$.

          If the canonically fitted unit circle $S^1 \subset S^n$ is removed from $S^n$, prove that the remaining space is homotopically equivalent to $S^{n-2}$.
*Remember that
$S^n := \{x \in \mathbb{R}^{n+1} : ||x|| = 1\}$.

$If the canonically fitted unit circle S^1 ⊂ S^n is removed from S^n, prove that the remaining space is homotopically equivalent to S^n-2. *Remember that S^n := {x ∈ℝ^n+1 : ||x|| = 1}.$

Added by Scott A.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Madhur L

12/16/2022

Step 1

The unit sphere Sn is defined as the set of all points in Rn+1 that are a distance of 1 from the origin. Mathematically, Sn is given by Sn = {x ∈ Rn+1 : ||x|| = 1}. Show more…

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THIS IS ALGEBRAIC TOPOLOGY AND GROUP THEORY. ADVANCED MATH.PLEASE, GIVE A TOTALLY ACCURATE ANSWER, STEP BY STEP AND WITH LUXURY OF DETAIL. THAT THE EXPERT WHO IS REALLY CONSISTING THE QUESTION KNOWS WHAT HE IS DOING. THE SOLUTION IS NOT URGENT, REASON FOR WHICH THE EXPERT MAY TAKE AS LONG AS I CONSIDER APPROPRIATE.*EITHER WAY, THANK YOU SO MUCH. THANK YOU IN ADVANCE FOR YOUR SUPPORT, TIME AND DEDICATION =). If the canonically fitted unit circle S1 c sn is removed from sn, prove that the *Remember that Sn={x E Rn+1:1|x|l=1}