An iterated sum formula for a spheroid's homotopy class modulo 2-torsion

Details An iterated sum formula for a spheroid's homotopy class modulo 2-torsion An iterated sum formula for a spheroid's homotopy class modulo 2-torsion

2006-06-21

arxiv.org/abs/math/0606528v1

Mathematics

Algebraic Topology

13 pages

Scientific paper

Let $X$ be a simply connected pointed space with finitely generated homotopy groups. Let $\Pi_n(X)$ denote the set of all continuous maps $a:I^n\to X$ taking $\partial I^n$ to the basepoint. For $a\in\Pi_n(X)$, let $[a]\in\pi_n(X)$ be its homotopy class. For an open set $E\subset I^n$, let $\Pi(E,X)$ be the set of all continuous maps $a:E\to X$ taking $E\cap\partial I^n$ to the basepoint. For a cover $\Gamma$ of $I^n$, let $\Gamma(r)$ be the set of all unions of at most $r$ elements of $\Gamma$. Put $r=(n-1)!$. We prove that for any finite open cover $\Gamma$ of $I^n$ there exist maps $f_E:\Pi(E,X)\to\pi_n(X)\otimes Z[1/2]$, $E\in\Gamma(r)$, such that $$ [a]\otimes1=\sum_{E\in\Gamma(r)} f_E(a|_E) $$ for all $a\in\Pi_n(X)$.

Affiliated with

Also associated with

No associations

Rating

An iterated sum formula for a spheroid's homotopy class modulo 2-torsion does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with An iterated sum formula for a spheroid's homotopy class modulo 2-torsion, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and An iterated sum formula for a spheroid's homotopy class modulo 2-torsion will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-622013