Some products involving the fourth Greek letter family element \tilde{d}s in the Adams spectral sequence

Xiugui LIU

Makale detayları

Some products involving the fourth Greek letter family element \tilde{d}s in the Adams spectral sequence

Yazarlar:

Xiugui LIU

Yayıncı:

TUBITAK

Dergi:

Turkish Journal of Mathematics 2011 Vol.35 Issue 2, pp.311-321

Belge Tipi:

Makale

Yayın Tarihi:

1/2011

Belge Dili:

Türkçe

Document ID (Org No.):

2000747991

Sıklık:

İki Aylık

eISSN:

1303-6149

pISSN:

1300-0098

Anahtar kelimeler:

Özet:

 

Let p be an odd prime and A be the mod p Steenrod algebra.  For computing the stable homotopy groups of spheres with the classical  Adams spectral sequence, we must compute the E2-term of the Adams  spectral sequence, ExtA\ast,\ast (Zp,Zp).  In this paper we prove  that in the cohomology of A, the product k0 hn \tilde d s + 4  \in ExtAs + 7, t(s,n) + s (Zp, Zp), is nontrivial for  n \geq 5, and trivial for n=3, 4, where \tildeds + 4 is  actually \tildeas + 4(4) described by Wang and Zheng, p  \geq 11, 0 \leq s < p - 4 and t(s,n)=2(p-1)[(s + 2) + (s + 4)p +   (s + 3)p2 + (s + 4)p3 + pn].

 

Let p be an odd prime and A be the mod p Steenrod algebra.  For computing the stable homotopy groups of spheres with the classical  Adams spectral sequence, we must compute the E2-term of the Adams  spectral sequence, ExtA\ast,\ast (Zp,Zp).  In this paper we prove  that in the cohomology of A, the product k0 hn \tilde d s + 4  \in ExtAs + 7, t(s,n) + s (Zp, Zp), is nontrivial for  n \geq 5, and trivial for n=3, 4, where \tildeds + 4 is  actually \tildeas + 4(4) described by Wang and Zheng, p  \geq 11, 0 \leq s < p - 4 and t(s,n)=2(p-1)[(s + 2) + (s + 4)p +   (s + 3)p2 + (s + 4)p3 + pn].

Makale detayları

Some products involving the fourth Greek letter family element \tilde{d}s in the Adams spectral sequence

Yazarlar:

Xiugui LIU

Yayıncı:

TUBITAK

Dergi:

Turkish Journal of Mathematics 2011 Vol.35 Issue 2, pp.311-321

Belge Tipi:

Makale

Yayın Tarihi:

1/2011

Belge Dili:

Türkçe

Document ID (Org No.):

2000747991

Sıklık:

İki Aylık

eISSN:

1303-6149

pISSN:

1300-0098

Key words: Steenrod algebra

cohomology

Adams spectral sequence

May spectral sequence

Sayı

Makale detayları

Some products involving the fourth Greek letter family element \tilde{d}s in the Adams spectral sequence

Yazarlar: Xiugui LIU

Yayıncı: TUBITAK

Dergi: Turkish Journal of Mathematics 2011 Vol.35 Issue 2, pp.311-321

Belge Tipi: Makale

Yayın Tarihi: 1/2011

Belge Dili: Türkçe

Document ID (Org No.): 2000747991

Sıklık: İki Aylık

eISSN: 1303-6149

pISSN: 1300-0098

Key words: Steenrod algebra

cohomology

Adams spectral sequence

May spectral sequence

Sayı

Yazarlar:

Xiugui LIU

Yayıncı:

TUBITAK

Dergi:

Turkish Journal of Mathematics 2011 Vol.35 Issue 2, pp.311-321

Belge Tipi:

Makale

Yayın Tarihi:

1/2011

Belge Dili:

Türkçe

Document ID (Org No.):

2000747991

Sıklık:

İki Aylık

eISSN:

1303-6149

pISSN:

1300-0098