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Mod p stable orders of finite CW-complexes

โœ Scribed by Huajian Yang

Publisher
Elsevier Science
Year
1996
Tongue
English
Weight
411 KB
Volume
73
Category
Article
ISSN
0166-8641

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โœฆ Synopsis

Let p be a prime and [X, X] the group consisting of classes of stable self-maps on a space X.

The mod p stable order of X denoted by 1x1, is defined to be the order of the stable identity map in the group [X, X] @ Z(,), where Z(,) is the ring of integers localized at p. Let X,"+" be a finite CW-complex with nontrivial cells of dimensions between n and n + k. In this paper we prove in Theorem 1.1 that IX,"fkIp 6 p[kI(2(~-'))l+V+E, where E = 0 if p is odd, and is 2 if p = 2, while v = min{j 1 P~H,(X~+~; Zc,)) = 0). As an application, we determine in Theorem 1.2 the mod p stable order of stunted lens spaces Lip_:") mod p", where p is an odd prime.

๐Ÿ“œ SIMILAR VOLUMES

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โœ V. Grolmusz ๐Ÿ“‚ Article ๐Ÿ“… 1995 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 504 KB

We prove in this paper that it is much harder to evaluate depth-2, size- \(N\) circuits with MOD \(m\) gates than with MOD \(p\) gates by \(k\)-party communication protocols: we show a \(k\)-party protocol which communicates \(O(1)\) bits to evaluate circuits with MOD \(p\) gates, while evaluating c

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Let 1 be a finitely generated subgroup of Q\* with rank r. We study the size of the order |1 p | of 1 mod p for density-one sets of primes. Using a result on the scarcity of primes p x for which p&1 has a divisor in an interval of the type [ y, y exp log { y] ({t0.15), we deduce that |1 p | p rร‚(r+1