• Journal of the Chungcheong Mathematical Society
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• v.19 no.4
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• pp.437-443
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• 2006

We study free actions of finite groups on the 3-dimensional nilmanifold for Type 1 and classify all such group actions, up to topological conjugacy. This work supplies missing one in [1, Theorem 3.11.].

• Journal of the Chungcheong Mathematical Society
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• v.20 no.3
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• pp.223-230
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• 2007

We study free actions of finite groups on the 3-dimensional nilmanifold and classify all such group actions, up to topological conjugacy. This work generalize Theorem 3.10 of [1].

• Journal of the Chungcheong Mathematical Society
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• v.10 no.1
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• pp.161-175
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• 1997

We classify free actions of finite abelian groups on the 3-dimensional nilmanifold, up to topological conjugacy. By the works of Bieberbach and Waldhausen, this classification problem is reduced to classifying all normal subgroups of almost Bieberbach groups of finite index, up to affine conjugacy.

• Journal of the Korean Mathematical Society
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• v.42 no.4
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• pp.795-826
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• 2005

We study free actions of finite abelian groups on 3­dimensional nilmanifolds. By the works of Bieberbach and Waldhausen, this classification problem is reduced to classifying all normal nilpotent subgroups of almost Bieberbach groups of finite index, up to affine conjugacy. All such actions are completely classified.

• Bulletin of the Korean Mathematical Society
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• v.58 no.1
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• pp.133-146
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• 2021

For pseudo-free and recurrent self-similar groups, we show that continuous orbit equivalence of inverse semigroup partial actions implies continuous orbit equivalence of group actions. Conversely, if group actions are continuous orbit equivalent, and the induced homeomorphism commutes with the shift maps on their groupoids, we obtain continuous orbit equivalence of inverse semigroup partial actions.

• Journal of the Chungcheong Mathematical Society
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• v.18 no.2
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• pp.223-232
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• 2005

We study only free actions of finite groups G on the 3-dimensional nilmanifold, up to topological conjugacy which yields an infra-nilmanifold of type 2.

• East Asian mathematical journal
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• v.35 no.3
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• pp.357-363
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• 2019

Let the circle act on a compact almost complex manifold M with a non-empty discrete fixed point set. To each fixed point, there are associated non-zero integers called weights. A positive weight w is called primitive if it cannot be written as the sum of positive weights, other than w itself. In this paper, we show that if every weight is primitive, then the Todd genus Todd(M) of M is positive and there are $Todd(M){\cdot}2^n$ fixed points, where dim M = 2n. This generalizes the result for symplectic semi-free actions by Tolman and Weitsman [8], the result for semi-free actions on almost complex manifolds by the author [6], and the result for certain symplectic actions by Godinho [1].

• Korean Journal of Cognitive Science
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• v.24 no.3
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• pp.237-270
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• 2013

Determinism and compatibilism have thought that libertarianism contradicts the scientific view. This paper demonstrates that the hypothesis that free will exists does not cause any problems and contradictions, while maintaining pro-scientific view. Rather, determinism lacks scientific and demonstrative bases. At first, I reject dualistic self by assuming identity theory of the self and physical body & brain. Free will is a functional concept or property that can have multiple realization. Therefore we can recognize whether aliens or robots have free will through observation on their acts. 'Free will' is a functional kinds term like 'digestion'. As we know we have digestive function, we can know that we have free will even before knowing the necessity of its existence by understanding micro structure of human free will. The judgement that an individual has free will function depends on whether it has particular actions. Those actions are controlling and restraining actions in context, predicting future, making elaborate conditional sentences, etc. Real being of free will is the physical occupant of the function that makes those actions. Determinism is based on various kinds of misconceptions and misunderstandings. Determinists often confuse necessity of physical law and determinism. Another decisive misunderstanding is that free will postulates same conditions and different results from the same point of time. However, free will postulates that the two points of time are different. Because determinism is unnecessary redundant hypothesis influenced by religions, according to Ockham's Razor, determinism should be eliminated.

• Journal of the Korean Mathematical Society
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• v.54 no.5
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• pp.1411-1440
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• 2017

We study free actions of finite groups on 3-dimensional nil-manifolds with the first homology ${\mathbb{Z}}^2{\oplus}{\mathbb{Z}}_p$. By the works of Bieberbach and Waldhausen, this classification problem is reduced to classifying all normal nilpotent subgroups of almost Bieberbach groups of finite index, up to affine conjugacy.

• The Pure and Applied Mathematics
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• v.14 no.4
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• pp.307-315
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• 2007

We study crossed products of the free group and semigroup $C^*-algebras$ by actions of ${\mathbb{R}$, i.e., flows, and estimate and compute their stable rank.