• Journal of the Chungcheong Mathematical Society
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• v.32 no.3
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• pp.365-381
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• 2019

We study free actions of finite nonabelian groups on 3-dimensional nilmanifolds with the first homology ${\mathbb{Z}}^2{\oplus}{\mathbb{Z}}_2$, up to topological conjugacy. We show that there exist three kinds of nonabelian group actions in ${\pi}_1$, two in ${\pi}_2$ or ${\pi}_{5,i}$(i = 1, 2, 3), one in the other cases, and clarify what those groups are.

• Journal of the Korean Mathematical Society
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• v.57 no.5
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• pp.1061-1078
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• 2020

We prove some results about the finiteness of co-associated primes of generalized local homology modules inspired by a conjecture of Grothendieck and a question of Huneke. We also show some equivalent properties of minimax local homology modules. By duality, we get some properties of Herzog's generalized local cohomology modules.

• Bulletin of the Korean Mathematical Society
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• v.53 no.3
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• pp.751-763
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• 2016

The properties of the nonabelian tensor products are interesting in different contexts of algebraic topology and group theory. We prove two theorems, dealing with the nonabelian tensor products of projective limits of finite groups. The first describes their topology. Then we show a result of embedding in the second homology group of a pro-p-group, via the notion of complete exterior centralizer. We end with some open questions, originating from these two results.

• Journal of the Korean Mathematical Society
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• v.39 no.1
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• pp.149-161
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• 2002

We study the torsions in the integral homology of the double loop space of the compact simple Lie groups by determining the higher Bockstein actions on the homology of those spaces through the Bockstein lemma and computing the Bockstein spectral sequence.

• Honam Mathematical Journal
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• v.24 no.1
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• pp.93-101
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• 2002

The $S^1$-Eule characteristics of X is defined by $\bar{\chi}_{S^1}(X)\;{\in}\;HH_1(ZG)$, where G is the fundamental group of connected finite $S^1$-compact manifold or connected finite $S^1$-finite complex X and $HH_1$ is the first Hochsch ild homology group functor. The purpose of this paper is to find several cases which the $S^1$-Euler characteristic has a homotopic invariant.

• Journal of the Korean Mathematical Society
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• v.56 no.5
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• pp.1265-1283
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• 2019

We develop a framework to construct geometric representations of finite groups G through the correspondence between real toric spaces $X^{\mathbb{R}}$ and simplicial complexes with characteristic matrices. We give a combinatorial description of the G-module structure of the homology of $X^{\mathbb{R}}$. As applications, we make explicit computations of the Weyl group representations on the homology of real toric varieties associated to the Weyl chambers of type A and B, which show an interesting connection to the topology of posets. We also realize a certain kind of Foulkes representation geometrically as the homology of real toric varieties.

• Honam Mathematical Journal
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• v.21 no.1
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• pp.157-169
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• 1999

For a k-connected inverse system $({\scr{X}},\;*)=((X_{\lambda},\;*),p_{{\lambda}{{\lambda}}^{\prime}},\;{\Lambda})$ of pointed topological spaces and pointed preserving weak fibrations, inducting epimorphic chain maps, over a directed set, we show that the homotopy group ${\pi}_k(lim{\scr{X}},\;*)$ of the inverse limit is isomorphic to the integral homology group $$H_k(lim{\scr{X}};\mathbb{Z})$. Using the result of S. $Marde{\check{s}}i{\acute{c}}$, we prove that the group of pure extension $Pext(colimH^n({\scr{X}},\;A)$ is isomorphic to the group of extension $Ext({\Delta}({\lambda}),\;Hom(H^n({\scr{X}}),\;A))$.

• Korean Journal of Poultry Science
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• v.27 no.2
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• pp.91-98
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• 2000

Phylogenetic tree constructed from the nucleotide sequences of the S1 gene showed that the 15 Korean strains of infectious bronchitis virus(IBV) examined were classified into 2 genetically distinct groups, except one respiratory strain, RB86, which was clustered with Massachusetts group. All the 5 respiratory strains belonged to Korean group I and the rest 9 nephropathogenic strains belonged to Korean group II according to the analysis, based on S1 gene sequences. Like previous classifications corresponded with the geographic origin, Korean stains were discriminated from geographically distinct reference strains of IBV. The nephropathogenic strains within Korean group IIsharing 96% homology were continuously isolated since 1990, and seemed to be genetically stable. Whereas the respiratory strains within Korean group Ⅰ sharing 88% homology were sporadically isolate since 1986m and seemed to be genetically unstable. Because we found putative accumulated point mutation as well as recombination events in Korean group Ⅰ, we discussed why genetic variations have often occurred in respiratory strains rather than nephropathognic strains.

• Communications of the Korean Mathematical Society
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• v.21 no.2
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• pp.337-345
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• 2006

John Harer conjectured that the canonical map from braid group to mapping class group induces zero homology homomorphism. To prove the conjecture it suffices to show that this map preserves the first Araki-Kudo-Dyer-Lashof operation. To get information on this homology operation we need to investigate the image of braiding under the Harer map. The main result of this paper is to give both algebraic and geometric interpretations of the image of braiding under the Harer map. For this we need to calculate long chains of consecutive actions of Dehn twists on the fundamental group of surface.

• Korean Journal of Plant Tissue Culture
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• v.26 no.1
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• pp.41-47
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• 1999

Phenylalanine ammonia-lyase (PAL; EC 4, 3, 1, 5) genomic clones were isolated from tomato(Lycopersicon esculentum L.) genomic DNA libraries using tomato PAL5 cDNA sequences as probes. The nucleotide sequences of tPAL1, tPAL4 and tPAL5 were compared. tPAL5 contains an open reading frame encoding a polypeptide of 722 amino acids, interrupted by a 710 bp intron in the codon for the amino acid 139. tPAL1 encodes a polypeptide of 249 amino acids which is much shorter than tPAL5 gene due to a premature stop codon and does not contain an intron. tPAL4 encodes a polypeptide of 357 amino acids, interrupted by a 305 bp intron in the codon for the amino acid 138. Premature stop codons observed in tPAL1 and tPAL4 gene produce a short polypeptide rather than a normal polypeptide (722 aa). tPALl shows 87.2% homology with tPAL4 and 85.3% homology with tPAL5 gene whereas tPAL4 showes 91.4% homology with tPAL5 at nucleotide level. In general, phylogenetic analysis showed that genes isolated from tomato, potato, and sweet potato were belong to the same group and another dicot plants such as parsley, bean, soybean, pea and alfalfa formed another group. PAL genes isolated from rice and yeast showed very low homology with other PAL genes and formed the other group.