• Journal of the Korean Mathematical Society
• /
• v.35 no.2
• /
• pp.281-294
• /
• 1998

In this paper, we extend the G-sequence of a CW-pair to the G-sequence of a map and show the existence of a map with nonexact G-sequence. We also give an example of a finite CW-pair with nontrivial $\omega$-homology in high order.

• Bulletin of the Korean Mathematical Society
• /
• v.36 no.4
• /
• pp.683-691
• /
• 1999

It has long been a question which homology class is represented by an embedded 2-sphere in a smooth 4-manifold. In this article we study the adjunction inequality, one of main results of Seiberg-Witten theory in smooth 4-manifolds, for an embedded 2-sphere. As a result, we give a criterion which homology class cannot be represented by an embedded 2-sphere in some cases.

• Korean Journal of Microbiology
• /
• v.29 no.5
• /
• pp.284-289
• /
• 1991

the nucleotide sequence of the 3' terminal 568 bases of the 18S rRNA gene from Mucor racemosus was determined. The 3' end of the structural gene was identified by comparison with the published sequence for the Saccharomyces cerevisiae gene. The M. racemosus gene was found to share 83.8% homology with that of S. cerevisiae and 71-81% homology with those of human, mouse, maize, Xenopus laevis and Tetrahymena thermophila. The known methylation sites in X. laevis and human were also highly conserved in M. racemosus and located within most conserved regions of 18S RNA gene throughout evolution.

• Bulletin of the Korean Mathematical Society
• /
• v.35 no.2
• /
• pp.235-258
• /
• 1998

We define a crossing of a link without referring to a specific projection of the link and describe a construction of a non-normalized Alexander polynomial associated to collections of such crossings of oriented links under an equivalence relation, called homology relation. The polynomial is computed from a special Seifert surface of the link. We prove that the polynomial is well-defined for the homology equivalence classes, investigate its relationship with the combinatorially defined Alexander polynomials and study some of its properties.

• Bulletin of the Korean Mathematical Society
• /
• v.53 no.3
• /
• pp.751-763
• /
• 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
• /
• v.39 no.6
• /
• pp.881-898
• /
• 2002

Our aim in this paper is to introduce a generalization of some notions in homological algebra. We define the concepts of chain U-complex, U-homology, chain (U, U')-map, chain (U, U')-homotopy and $\mu$-functor. We also obtain some interesting results. We use these results to find a generalization of Lambek Lemma, Snake Lemma, Connecting Homomorphism and Exact Triangle.

• Journal of the Korean Mathematical Society
• /
• v.48 no.4
• /
• pp.749-774
• /
• 2011

Given a Morse function on a manifold whose moduli spaces of gradient flow lines for each action window are compact up to breaking one gets a bidirect system of chain complexes. There are different possibilities to take limits of such a bidirect system. We discuss in this note the relation between these different limits.

• Bulletin of the Korean Mathematical Society
• /
• v.41 no.2
• /
• pp.387-391
• /
• 2004

Let A be Noetherian ring, a= (${\tau}_1..., \tau_n$ an ideal of A and $C_{A}$ be category of A-modules and A-homomorphisms. We show that the connected left sequences of covariant functors ${limH_i(K.(t^t,-))}_{i\geq0}$ and ${lim{{Tor^A}_i}(\frac{A}{a^f}-)}_{i\geq0}$ are isomorphic from $C_A$ to itself, where $\tau^t\;=\;{{\tau_^t}_1$, ㆍㆍㆍ${\tau^t}_n$.

• Bulletin of the Korean Mathematical Society
• /
• v.54 no.1
• /
• pp.1-15
• /
• 2017

Kanenobu has given infinite families of knots with the same HOMFLY polynomial invariant but distinct Alexander module structure. In this paper, we give a recursive formula for the Khovanov cohomology of all Kanenobu knots K(p, q), where p and q are integers. The result implies that the rank of the Khovanov cohomology of K(p, q) is an invariant of p + q. Our computation uses only the basic long exact sequence in knot homology and some results on homologically thin knots.

• BMB Reports
• /
• v.41 no.6
• /
• pp.444-447
• /
• 2008

Trypanothione reductase is an important target enzyme for structure-based drug design against Leishmania. We used homology modeling to construct a three-dimensional structure of the trypanothione reductase (TR) of Leishmania infantum. The structure shows acceptable Ramachandran statistics and a remarkably different active site from glutathione reductase(GR). Thus, a specific inhibitor against TR can be designed without interfering with host (human) GR activity.