Local Coefficients Revisited
Two simple "simplicial approximation" tricks are invoked to prove basic results involving (co)-homology with local coefficients.
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arXiv subjects
Fang Sun
Publications and source records attributed to Fang Sun.
An elementary proof for Poincare Duality with local coefficients
An proof of Poincare Duality with local coefficients and with compact support is provided. The proof does not require Sheaf Theory or anything equivalent and is thus more accessible for the general audience.
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Manifolds with the fixed point property and their squares
The Cartesian squares (powers) of manifolds with the fixed point property (f.p.p.) are considered. Examples of manifolds with the f.p.p. are constructed whose symmetric squares fail to have the f.p.p..
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Topological Symmetries of R^3, II
If a fintie group G acts topologically and faithfully on R^3, then G is a subgroup of O(3)
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Topological Symmetries of R^3
If a finite group acts topologically, faithfully and orientation preservingly on R^3, then it is isomorphic to a subgroup of SO(3).
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On the unsplittable minimal zero-sum sequences over finite cyclic groups of prime order
Let $p > 155$ be a prime and let $G$ be a cyclic group of order $p$. Let $S$ be a minimal zero-sum sequence with elements over $G$, i.e., the sum of elements in $S$ is zero, but no proper nontrivial subsequence of $S$ has sum zero. We call $S$ is unsplittable, if there do not exist $g$ in $S$ and $x,y \in G$ such that $g=x+y$ and $Sg^{-1}xy$ is also a minimal zero-sum sequence. In this paper we show that if $S$ is an unsplittable minimal zero-sum sequence of length $|S|= \frac{p-1}{2}$, then $S=g^{\frac{p-11}{2}}(\frac{p+3}{2}g)^4(\frac{p-1}{2}g)$ or $g^{\frac{p-7}{2}}(\frac{p+5}{2}g)^2(\frac{p-3}{2}g)$. Furthermore, if $S$ is a minimal zero-sum sequence with $|S| \ge \frac{p-1}{2}$, then $\ind(S) \leq 2$.
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