ترغب بنشر مسار تعليمي؟ اضغط هنا

On the May Spectral Sequence at the prime 2

176   0   0.0 ( 0 )
 نشر من قبل Weinan Lin
 تاريخ النشر 2020
  مجال البحث
والبحث باللغة English
 تأليف Weinan Lin




اسأل ChatGPT حول البحث

We make a conjecture about all the relations in the $E_2$ page of the May spectral sequence and prove it in a subalgebra which covers a large range of dimensions. We conjecture that the $E_2$ page is nilpotent free and also prove it in this subalgebra. For further computations we construct maps of spectral sequences which systematically extend one of the techniques used by May and Tangora.



قيم البحث

اقرأ أيضاً

In previous work of the first author and Jibladze, the $E_3$-term of the Adams spectral sequence was described as a secondary derived functor, defined via secondary chain complexes in a groupoid-enriched category. This led to computations of the $E_3 $-term using the algebra of secondary cohomology operations. In work with Blanc, an analogous description was provided for all higher terms $E_m$. In this paper, we introduce $2$-track algebras and tertiary chain complexes, and we show that the $E_4$-term of the Adams spectral sequence is a tertiary Ext group in this sense. This extends the work with Jibladze, while specializing the work with Blanc in a way that should be more amenable to computations.
132 - Mark Behrens , Kyle Ormsby 2012
We study modular approximations Q(l), l = 3,5, of the K(2)-local sphere at the prime 2 that arise from l-power degree isogenies of elliptic curves. We develop Hopf algebroid level tools for working with Q(l) and record Hill, Hopkins, and Ravenels com putation of the homotopy groups of TMF_0(5). Using these tools and formulas of Mahowald and Rezk for Q(3) we determine the image of Shimomuras 2-primary divided beta-family in the Adams-Novikov spectral sequences for Q(3) and Q(5). Finally, we use low-dimensional computations of the homotopy of Q(3) and Q(5) to explore the role of these spectra as approximations to the K(2)-local sphere.
196 - Agnes Beaudry 2017
In this note, we compute the image of the $alpha$-family in the homotopy of the $K(2)$-local sphere at the prime $p=2$ by locating its image in the algebraic duality spectral sequence. This is a stepping stone for the computation of the homotopy grou ps of the $K(2)$-local sphere at the prime $2$ using the duality spectral sequences.
Let M(1) be the mod 2 Moore spectrum. J.F. Adams proved that M(1) admits a minimal v_1-self map v_1^4: Sigma^8 M(1) -> M(1). Let M(1,4) be the cofiber of this self-map. The purpose of this paper is to prove that M(1,4) admits a minimal v_2-self map o f the form v_2^32: Sigma^192 M(1,4) -> M(1,4). The existence of this map implies the existence of many 192-periodic families of elements in the stable homotopy groups of spheres.
A multicomplex, also known as a twisted chain complex, has an associated spectral sequence via a filtration of its total complex. We give explicit formulas for all the differentials in this spectral sequence.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا