Nilpotent $n$-tuples in $SU(2)$ Article Swipe

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Omar Antolín Camarena , Bernardo Villarreal ·

YOU? · · 2016 · Open Access · · DOI: https://doi.org/10.48550/arxiv.1611.05937

We describe the connected components of the space $\text{Hom}(Γ,SU(2))$ of homomorphisms for a discrete nilpotent group $Γ$. The connected components arising from homomorphisms with non-abelian image turn out to be homeomorphic to $\mathbb{RP}^3$. We give explicit calculations when $Γ$ is a finitely generated free nilpotent group. In the second part of the paper we study the filtration $B_{\text{com}}SU(2) = B(2,SU(2))\subset\cdots \subset B(q,SU(2))\subset\cdots$ of the classifying space $BSU(2)$ (introduced by Adem, Cohen and Torres-Giese), showing that for every $q\geq2$, the inclusions induce a homology isomorphism with coefficients over a ring in which 2 is invertible. Most of the computations are done for $SO(3)$ and $U(2)$ as well.

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Homomorphism Invertible matrix Nilpotent Classifying space Mathematics Abelian group Isomorphism (crystallography) Tuple Homology (biology) Nilpotent group Group (periodic table) Combinatorics Pure mathematics Algebra over a field Discrete mathematics Cohomology Physics Crystallography Chemistry Quantum mechanics Biochemistry Crystal structure Gene

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Type: preprint
Language: en
Landing Page: http://arxiv.org/abs/1611.05937
PDF: https://arxiv.org/pdf/1611.05937
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DOI: https://doi.org/10.48550/arxiv.1611.05937

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Title: Nilpotent $n$-tuples in $SU(2)$

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Authors: Omar Antolín Camarena, Bernardo Villarreal

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Concepts: Homomorphism, Invertible matrix, Nilpotent, Classifying space, Mathematics, Abelian group, Isomorphism (crystallography), Tuple, Homology (biology), Nilpotent group, Group (periodic table), Combinatorics, Pure mathematics, Algebra over a field, Discrete mathematics, Cohomology, Physics, Crystallography, Chemistry, Quantum mechanics, Biochemistry, Crystal structure, Gene

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Cited by: 1

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abstract_inverted_index.isomorphism	83
abstract_inverted_index.non-abelian	24
abstract_inverted_index.calculations	36
abstract_inverted_index.coefficients	85
abstract_inverted_index.computations	97
abstract_inverted_index.homeomorphic	30
abstract_inverted_index.homomorphisms	10, 22
abstract_inverted_index.Torres-Giese),	72
abstract_inverted_index.$\mathbb{RP}^3$.	32
abstract_inverted_index.$B_{\text{com}}SU(2)	57
abstract_inverted_index.$\text{Hom}(Γ,SU(2))$	8
abstract_inverted_index.B(2,SU(2))\subset\cdots	59
abstract_inverted_index.B(q,SU(2))\subset\cdots$	61
cited_by_percentile_year.max	94
cited_by_percentile_year.min	90
countries_distinct_count	0
institutions_distinct_count	2
sustainable_development_goals[0].id	https://metadata.un.org/sdg/10
sustainable_development_goals[0].score	0.4300000071525574
sustainable_development_goals[0].display_name	Reduced inequalities
citation_normalized_percentile.value	0.74552705
citation_normalized_percentile.is_in_top_1_percent	False
citation_normalized_percentile.is_in_top_10_percent	False