scholarly journals THE UNIT MAP OF THE ALGEBRAIC SPECIAL LINEAR COBORDISM SPECTRUM

2019 ◽  
pp. 1-26
Author(s):  
Maria Yakerson
Keyword(s):  
Explicit Description ◽  
Homotopy Groups ◽  
Joint Work ◽  
Loop Spaces ◽  
Special Linear ◽  
Generators And Relations ◽  
Thom Spectra

In the joint work with Elmanto, Hoyois, Khan and Sosnilo, we computed infinite $\mathbb{P}^{1}$ -loop spaces of motivic Thom spectra using the technique of framed correspondences. This result allows us to express non-negative $\mathbb{G}_{m}$ -homotopy groups of motivic Thom spectra in terms of geometric generators and relations. Using this explicit description, we show that the unit map of the algebraic special linear cobordism spectrum induces an isomorphism on $\mathbb{G}_{m}$ -homotopy sheaves.

On Localized Unstable K1-groups and Applications to Self-homotopy Groups

2014 ◽  
Vol 57 (2) ◽  
pp. 344-356
Author(s):  
Daisuke Kishimoto ◽  
Akira Kono ◽  
Mitsunobu Tsutaya
Keyword(s):  
Homotopy Group ◽  
The Self ◽  
Explicit Description ◽  
Homotopy Groups

AbstractThe method for computing the p-localization of the group [X, U(n)], by Hamanaka in 2004, is revised. As an application, an explicit description of the self-homotopy group of Sp(3) localized at p ≥ 5 is given and the homotopy nilpotency of Sp(3) localized at p ≥ 5 is determined.

scholarly journals COENDOMORPHISM LEFT BIALGEBROIDS

2012 ◽  
Vol 12 (03) ◽  
pp. 1250181
Author(s):  
A. ARDIZZONI ◽  
L. EL KAOUTIT ◽  
C. MENINI
Keyword(s):  
Explicit Description ◽  
Rigorous Proof ◽  
Generators And Relations

The main purpose of this paper is to give a rigorous proof of the construction of coendomorphism left bialgebroids as well as an explicit description of their structure maps. We also compute some concrete examples of these objects by means of their generators and relations.

ON THE COHOMOLOGY OF $\bar{\mathcal M}_{0,n}({\mathbb P}^1,d)$

2002 ◽  
Vol 04 (04) ◽  
pp. 751-761 ◽  
Author(s):  
GILBERTO BINI ◽  
CLAUDIO FONTANARI
Keyword(s):  
Moduli Space ◽  
Cohomology Group ◽  
Betti Numbers ◽  
Projective Line ◽  
Explicit Description ◽  
Vanishing Theorems ◽  
Generators And Relations ◽  
Rational Cohomology ◽  
Complex Projective Line ◽  
Complex Projective

Here we investigate rational cohomology of the moduli space of stable maps to the complex projective line with a purely algebro-pgeometric approach. In particular, we prove vanishing theorems for all its odd Betti numbers, and we give an explicit description by generators and relations of its second cohomology group.

On the Semi-Tensor Product of the Dyer-Lashof and Steenrod Algebras

1989 ◽  
Vol 41 (4) ◽  
pp. 676-701
Author(s):  
H. E. A. Campbell ◽  
P. S. Selick
Keyword(s):  
Hopf Algebra ◽  
Tensor Product ◽  
Vector Space ◽  
Steenrod Algebra ◽  
Joint Work ◽  
Loop Spaces ◽  
Joint Structure ◽  
Infinite Loop Spaces ◽  
Infinite Loop ◽  
Adem Relations

This paper arises out of joint work with F. R. Cohen and F. P. Peterson [5, 2, 3] on the joint structure of infinite loop spaces QX. The homology of such a space is operated on by both the Dyer-Lashof algebra, R, and the opposite of the Steenrod algebra A∗. We describe a convenient summary of these actions; let M be the algebra which is R ⊗ A∗ as a vector space and where multiplication Q1 ⊗ PJ. Q1’ ⊗ PJ’∗ is given by applying the Nishida relations in the middle and then the appropriate Adem relations on the ends. Then M is a Hopf algebra which acts on the homology of infinite loop spaces.

James-Hopf Invariants, Anick’s Spaces, and the Double Loops on Odd Primary Moore Spaces

2000 ◽  
Vol 43 (2) ◽  
pp. 226-235
Author(s):  
Joseph Neisendorfer
Keyword(s):  
Homotopy Groups ◽  
Dimensional Sphere ◽  
Double Loop ◽  
Loop Spaces ◽  
Moore Space ◽  
Moore Spaces ◽  
Hopf Invariants

AbstractUsing spaces introduced by Anick, we construct a decomposition into indecomposable factors of the double loop spaces of odd primary Moore spaces when the powers of the primes are greater than the first power. If n is greater than 1, this implies that the odd primary part of all the homotopy groups of the 2n + 1 dimensional sphere lifts to a mod pr Moore space.

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