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Braids and symplectic four-manifolds with abelian fundamental group
four-manifolds abelian fundamental group
2010/3/1
We explain how a version of Floer homology can be used as an invariant of symplectic manifolds with b1>0. As a concrete example, we look at four-manifolds produced from braids by a surgery constructio...
We describe here a new concept of one group chasing another, called "group chase and escape", by presenting a simple model. We will show that even a simple model can demonstrate rather rich and comple...
Trace Classes and Fixed Points for the Extended Modular Group \overline{G}
Extended modular group trace class fixed points
2010/2/25
The extended modular group \overline{G}=PGL(2,\mathbb{Z}) is the group obtained by adding the reflection R(z)=1/\overline{z} to the generators of the modular group G =PSL(2, {Z}). In this paper, we fi...
On the Power Subgroups of the Extended Modular Group \overline{G}
the Extended Modular Group Power Subgroups
2010/2/26
On the Power Subgroups of the Extended Modular Group \overline{G}。
A Borsuk-Ulak Theorem for Heisenberg Group Actions
Borsuk-Ulam Type Theorem Cohomological Index Group Action
2010/3/1
Let G=H2n+1 be a (2n+1)-dimensional Heisenberg Lie group acts on M=Cm-\{0\} and M'=Cm'-\{0\} exponentially. By using Cohomological Index we proved the following theorem. If f:M{\to}M' is a G-equivaria...
Bogoliubov Renormalization Group and Symmetry of Solution in Mathematical Physics
Bogoliubov Renormalization Group Mathematical Physics
2010/11/2
Evolution of the concept known in the theoretical physics as the Renormalization Group (RG) is presented. The corresponding symmetry, that has been first introduced in QFT in mid-fifties, is a contin...