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Abstract
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We define and study a homotopy invariant called the connectivity
weight to compute the weighted length between spaces
and
. This is an invariant based
on the connectivity of
,
where
is a space attached in a mapping cone sequence from
to
. We
use the Lusternik–Schnirelmann category to prove a theorem concerning
the connectivity of all spaces attached in any decomposition from
to
.
This theorem is used to prove that for any positive rational number
, there is a
space
such that
, the connectivity
weighted cone-length of
.
We compute
and
for many spaces and give several examples.
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Keywords
Lusternik–Schnirelmann category, categorical sequence, cone
length, killing length, Egyptian fractions, mapping cone
sequence
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Mathematical Subject Classification 2010
Primary: 55M30, 55P05
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Publication
Received: 25 August 2011
Revised: 8 December 2011
Accepted: 8 December 2011
Published: 20 March 2012
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