A CONTRACTING HOMOTOPY FOR BARDZELL'S RESOLUTION

2008 ◽  
Vol 108A (2) ◽  
pp. 111-117
Author(s):  
Emil Sköldberg
Keyword(s):  
Contracting Homotopy

scholarly journals The strong Suslin reciprocity law

2021 ◽  
Vol 157 (4) ◽  
pp. 649-676
Author(s):  
Daniil Rudenko
Keyword(s):  
Rational Functions ◽  
Projective Curve ◽  
Main Ingredient ◽  
Homotopy Invariance ◽  
Reciprocity Law ◽  
Hyperbolic Volume ◽  
Scissors Congruence ◽  
Dehn Invariant ◽  
Contracting Homotopy ◽  
Invariance Theorem

We prove the strong Suslin reciprocity law conjectured by A. Goncharov. The Suslin reciprocity law is a generalization of the Weil reciprocity law to higher Milnor $K$ -theory. The Milnor $K$ -groups can be identified with the top cohomology groups of the polylogarithmic motivic complexes; Goncharov's conjecture predicts the existence of a contracting homotopy underlying Suslin reciprocity. The main ingredient of the proof is a homotopy invariance theorem for the cohomology of the polylogarithmic motivic complexes in the ‘next to Milnor’ degree. We apply these results to the theory of scissors congruences of hyperbolic polytopes. For every triple of rational functions on a compact projective curve over $\mathbb {C}$ we construct a hyperbolic polytope (defined up to scissors congruence). The hyperbolic volume and the Dehn invariant of this polytope can be computed directly from the triple of rational functions on the curve.

scholarly journals Application of Two Rowed Weyl Module in the Case of Partition (6, 6)/(1,U) when U= 0,1

2021 ◽  
pp. 4071-4080
Author(s):  
Alaa Abbas Mansour ◽  
Haytham R. Hassan
Keyword(s):  
Weyl Module ◽  
Contracting Homotopy

The main aim of this paper is to study the application of Weyl module resolution in the case of two rows, which will be specified in the skew- partition (6, 6)/(1,1) and (6,6)/(1,0), by using the homological Weyl (i.e. the contracting homotopy and place polarization).

scholarly journals Resolution for the two-rowed weyl module inThe cases of (6,5) / (1,0) and (6,5) / (2,0)

2020 ◽  
pp. 416-421
Author(s):  
Annam Ali Abbas ◽  
Haytham R. Hassan
Keyword(s):  
Weyl Module ◽  
Contracting Homotopy

     The main purpose of this paper is to study the application of weyl module and resolution in the case skew- shapes (6, 5) / (1, 0) and (6, 5) / (2, 0) by using contracting homotopy and the place polarization.

scholarly journals Free Crossed Resolutions of Groups and Presentations of Modules of Identities among Relations

1999 ◽  
Vol 2 ◽  
pp. 28-61 ◽  
Author(s):  
Ronald Brown ◽  
Abdul Razak Salleh
Keyword(s):  
Cayley Graph ◽  
Universal Cover ◽  
Partial Resolution ◽  
Contracting Homotopy ◽  
Special Case

AbstractThe paper gives formulae for a module presentation of the module of identities among relations for a presentation of a group, in terms of information on 0- and 1-combings of the Cayley graph. These formulae are seen as a special case of formulae for extending a partial free crossed resolution of a group, given a partial contracting homotopy of the universal cover of the partial resolution.

scholarly journals Application of Two Rowed Weyl Module in the Case of Partition (7,6) and Skew- Partition (7,6)/(1,0)

2021 ◽  
pp. 3071-3080
Author(s):  
Nejood A. Hatim ◽  
Haytham R. Hassan
Keyword(s):  
Weyl Module ◽  
Contracting Homotopy

The aim of this work is to study the application of Weyl module resolution in the case of two rows, which will be specified in the partition (7, 6) and skew- partition (7,6)/(1,0)  by using the homological Weyl (i.e. the contracting homotopy and place polarization).

scholarly journals Application of the Two Rowed Weyl Module in the Case of Partitions (7,7) and (7, 7) / (1, 0)

2020 ◽  
pp. 1123-1135
Author(s):  
Nubras Yasir Khudair ◽  
Haytham Razooki Hassan
Keyword(s):  
Weyl Module ◽  
Contracting Homotopy

The purpose of this paper is to study the application of Weyl module’s resolution in the case of two rows which will be specified in the partitions (7, 7) and (7, 7) / (1, 0), using the homological Weyl (i.e. the contracting homotopy and place polarization).

Simplicial (Co)-homology of

2018 ◽  
Vol 62 (4) ◽  
pp. 756-766
Author(s):  
Yasser Farhat ◽  
Frédéric Gourdeau
Keyword(s):  
Linear Operator ◽  
Banach Algebra ◽  
Bounded Linear Operator ◽  
Banach Algebras ◽  
Cyclic Cohomology ◽  
Cohomology Groups ◽  
Bounded Linear ◽  
Contracting Homotopy ◽  
Unital Banach Algebra

AbstractWe consider the unital Banach algebra $\ell ^{1}(\mathbb{Z}_{+})$ and prove directly, without using cyclic cohomology, that the simplicial cohomology groups ${\mathcal{H}}^{n}(\ell ^{1}(\mathbb{Z}_{+}),\ell ^{1}(\mathbb{Z}_{+})^{\ast })$ vanish for all $n\geqslant 2$. This proceeds via the introduction of an explicit bounded linear operator which produces a contracting homotopy for $n\geqslant 2$. This construction is generalised to unital Banach algebras $\ell ^{1}({\mathcal{S}})$, where ${\mathcal{S}}={\mathcal{G}}\cap \mathbb{R}_{+}$ and ${\mathcal{G}}$ is a subgroup of $\mathbb{R}_{+}$.

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