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Jonathan Spreer - One of the best experts on this subject based on the ideXlab platform.
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A Polynomial-Time Algorithm to Compute Turaev–Viro Invariants $$\mathrm {TV}_{4,q}$$ TV 4 , q of 3-Manifolds with Bounded First Betti Number
Foundations of Computational Mathematics, 2020Co-Authors: Clément Maria, Jonathan SpreerAbstract:In this article, we introduce a fixed-parameter tractable algorithm for computing the Turaev–Viro invariants $$\mathrm {TV}_{4,q}$$ TV 4 , q , using the first Betti number, i.e. the dimension of the first Homology Group of the manifold with $$\mathbb {Z}_2$$ Z 2 -coefficients, as parameter. This is, to our knowledge, the first parameterised algorithm in computational 3-manifold topology using a topological parameter. The computation of $$\mathrm {TV}_{4,q}$$ TV 4 , q is known to be #P-hard in general; using a topological parameter provides an algorithm polynomial in the size of the input triangulation for the family of 3-manifolds with first $$\mathbb {Z}_2$$ Z 2 -Homology Group of bounded dimension. Our algorithm is easy to implement, and running times are comparable with running times to compute integral Homology Groups for standard libraries of triangulated 3-manifolds. The invariants we can compute this way are powerful: in combination with integral Homology and using standard data sets, we are able to almost double the pairs of 3-manifolds we can distinguish. We hope this qualifies $$\mathrm {TV}_{4,q}$$ TV 4 , q to be added to the short list of standard properties (such as orientability, connectedness and Betti numbers) that can be computed ad hoc when first investigating an unknown triangulation.
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A Polynomial-Time Algorithm to Compute Turaev–Viro Invariants $$\mathrm {TV}_{4,q}$$TV4,q of 3-Manifolds with Bounded First Betti Number
Foundations of Computational Mathematics, 2019Co-Authors: Clément Maria, Jonathan SpreerAbstract:In this article, we introduce a fixed-parameter tractable algorithm for computing the Turaev–Viro invariants $$\mathrm {TV}_{4,q}$$ TV 4 , q , using the first Betti number, i.e. the dimension of the first Homology Group of the manifold with $$\mathbb {Z}_2$$ Z 2 -coefficients, as parameter. This is, to our knowledge, the first parameterised algorithm in computational 3-manifold topology using a topological parameter. The computation of $$\mathrm {TV}_{4,q}$$ TV 4 , q is known to be #P-hard in general; using a topological parameter provides an algorithm polynomial in the size of the input triangulation for the family of 3-manifolds with first $$\mathbb {Z}_2$$ Z 2 -Homology Group of bounded dimension. Our algorithm is easy to implement, and running times are comparable with running times to compute integral Homology Groups for standard libraries of triangulated 3-manifolds. The invariants we can compute this way are powerful: in combination with integral Homology and using standard data sets, we are able to almost double the pairs of 3-manifolds we can distinguish. We hope this qualifies $$\mathrm {TV}_{4,q}$$ TV 4 , q to be added to the short list of standard properties (such as orientability, connectedness and Betti numbers) that can be computed ad hoc when first investigating an unknown triangulation.
Clément Maria - One of the best experts on this subject based on the ideXlab platform.
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A Polynomial-Time Algorithm to Compute Turaev–Viro Invariants $$\mathrm {TV}_{4,q}$$ TV 4 , q of 3-Manifolds with Bounded First Betti Number
Foundations of Computational Mathematics, 2020Co-Authors: Clément Maria, Jonathan SpreerAbstract:In this article, we introduce a fixed-parameter tractable algorithm for computing the Turaev–Viro invariants $$\mathrm {TV}_{4,q}$$ TV 4 , q , using the first Betti number, i.e. the dimension of the first Homology Group of the manifold with $$\mathbb {Z}_2$$ Z 2 -coefficients, as parameter. This is, to our knowledge, the first parameterised algorithm in computational 3-manifold topology using a topological parameter. The computation of $$\mathrm {TV}_{4,q}$$ TV 4 , q is known to be #P-hard in general; using a topological parameter provides an algorithm polynomial in the size of the input triangulation for the family of 3-manifolds with first $$\mathbb {Z}_2$$ Z 2 -Homology Group of bounded dimension. Our algorithm is easy to implement, and running times are comparable with running times to compute integral Homology Groups for standard libraries of triangulated 3-manifolds. The invariants we can compute this way are powerful: in combination with integral Homology and using standard data sets, we are able to almost double the pairs of 3-manifolds we can distinguish. We hope this qualifies $$\mathrm {TV}_{4,q}$$ TV 4 , q to be added to the short list of standard properties (such as orientability, connectedness and Betti numbers) that can be computed ad hoc when first investigating an unknown triangulation.
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A Polynomial-Time Algorithm to Compute Turaev–Viro Invariants $$\mathrm {TV}_{4,q}$$TV4,q of 3-Manifolds with Bounded First Betti Number
Foundations of Computational Mathematics, 2019Co-Authors: Clément Maria, Jonathan SpreerAbstract:In this article, we introduce a fixed-parameter tractable algorithm for computing the Turaev–Viro invariants $$\mathrm {TV}_{4,q}$$ TV 4 , q , using the first Betti number, i.e. the dimension of the first Homology Group of the manifold with $$\mathbb {Z}_2$$ Z 2 -coefficients, as parameter. This is, to our knowledge, the first parameterised algorithm in computational 3-manifold topology using a topological parameter. The computation of $$\mathrm {TV}_{4,q}$$ TV 4 , q is known to be #P-hard in general; using a topological parameter provides an algorithm polynomial in the size of the input triangulation for the family of 3-manifolds with first $$\mathbb {Z}_2$$ Z 2 -Homology Group of bounded dimension. Our algorithm is easy to implement, and running times are comparable with running times to compute integral Homology Groups for standard libraries of triangulated 3-manifolds. The invariants we can compute this way are powerful: in combination with integral Homology and using standard data sets, we are able to almost double the pairs of 3-manifolds we can distinguish. We hope this qualifies $$\mathrm {TV}_{4,q}$$ TV 4 , q to be added to the short list of standard properties (such as orientability, connectedness and Betti numbers) that can be computed ad hoc when first investigating an unknown triangulation.
Decheng Yang - One of the best experts on this subject based on the ideXlab platform.
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clostridium ljungdahlii sp nov an acetogenic species in clostridial rrna Homology Group i
International Journal of Systematic and Evolutionary Microbiology, 1993Co-Authors: Ralph S Tanner, Letrisa M Miller, Decheng YangAbstract:Clostridium ljungdahlii sp. nov. strain ATCC 49587T (T = type strain) was isolated from chicken yard waste for its ability to produce ethanol from synthesis gas. This gram-positive, motile, sporeforming rod's metabolism was primarily acetogenic. C. ljungdahlii grew with carbon monoxide, hydrogen and carbon dioxide, ethanol, pyruvate, arabinose, xylose, fructose, or glucose. Methanol, ferulic acid, lactate, galactose, and mannose did not support growth. The G+C content was 22 to 23 mol%. C. ljungdahlii is the first acetogen in clostridial 23S rRNA Homology Group I.
Andrew Putman - One of the best experts on this subject based on the ideXlab platform.
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Equivariant Group presentations and the second Homology Group of the Torelli Group
Mathematische Annalen, 2019Co-Authors: Martin Kassabov, Andrew PutmanAbstract:We develop a theory of equivariant Group presentations and relate them to the second Homology Group of a Group. Our main application says that the second Homology Group of the Torelli subGroup of the mapping class Group is finitely generated as a \(\mathbb {Z}[{{\,\mathrm{Sp}\,}}_{2g}(\mathbb {Z})]\)-module.
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on the second Homology Group of the torelli subGroup of aut fn
Geometry & Topology, 2017Co-Authors: Matthew B Day, Andrew PutmanAbstract:Let IA_n be the Torelli subGroup of Aut(F_n). We give an explicit finite set of generators for H_2(IA_n) as a GL_n(Z)-module. Corollaries include a version of surjective representation stability for H_2(IA_n), the vanishing of the GL_n(Z)-coinvariants of H_2(IA_n), and the vanishing of the second rational Homology Group of the level l congruence subGroup of Aut(F_n). Our generating set is derived from a new Group presentation for IA_n which is infinite but which has a simple recursive form.
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the second rational Homology Group of the moduli space of curves with level structures
Advances in Mathematics, 2012Co-Authors: Andrew PutmanAbstract:Abstract Let Γ be a finite-index subGroup of the mapping class Group of a closed genus g surface that contains the Torelli Group. For instance, Γ can be the level L subGroup or the spin mapping class Group. We show that H 2 ( Γ ; Q ) ≅ Q for g ⩾ 5 . A corollary of this is that the rational Picard Groups of the associated finite covers of the moduli space of curves are equal to Q . We also prove analogous results for surface with punctures and boundary components.
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the second rational Homology Group of the moduli space of curves with level structures
arXiv: Geometric Topology, 2008Co-Authors: Andrew PutmanAbstract:Let $\Gamma$ be a finite-index subGroup of the mapping class Group of a closed genus $g$ surface that contains the Torelli Group. For instance, $\Gamma$ can be the level $L$ subGroup or the spin mapping class Group. We show that $H_2(\Gamma;\Q) \cong \Q$ for $g \geq 5$. A corollary of this is that the rational Picard Groups of the associated finite covers of the moduli space of curves are equal to $\Q$. We also prove analogous results for surface with punctures and boundary components.
Tomohiko Fujisawa - One of the best experts on this subject based on the ideXlab platform.
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streptococcus gallolyticus sp nov gallate degrading organisms formerly assigned to streptococcus bovis
Systematic and Applied Microbiology, 1995Co-Authors: Ro Osawa, Tomohiko FujisawaAbstract:Summary Phenotypic charcteristics including the abilites two hydrolyze tannin and to decarboxylate gallic acid in 31 strains of S. bovis and 3 strains of S. equinus were compared with their dexoyribonucleic acid (DNA) relatedness. It was found that the strains capable of decarboxylating gallic acid all belong to a single DNA Homology Group which does not include either the type strain of S. bovis or the type strain of S. equinus . Thus it was concluded that the gallate degrading strains of S. bovis should be re-assigned to a new species, for which the name Streptococcus gallolyticus sp. nov. is proposed.