论文标题
REEB图，超曲面系统和表达系统与自由组之间的关系
Relations between Reeb graphs, systems of hypersurfaces and epimorphisms onto free groups
论文作者
论文摘要
我们从$φ_1（m）\ colonπ_1（m）\ to f_r $之间构建了一个对应关系，从紧凑型歧管$ m $的基本组中构建到自由等级$ r $的组，以及$ r $ r $ r $ framed nontareparame nor-framed nor-framed nor-framed nor-framed in n $ m $中的系统，这会导致对这些系统的cobord cobord systems coldextions of Systems of Systems of Systems of Systems of Systems of Systems of Systems。因此，对于封闭的流形，任何这样的$φ$都可以用莫尔斯函数的reeb表达$ f \ colon m \ to \ mathbb {r} $，即，由由商$ m \ to \ mathcal {r} $ to phage the reeeb of reeeb of reeeb的商人$ m \ to to \ mathcal $ m \ to reeeb of $ f $ f $ f $。应用这种结构，我们讨论了分类的问题，直到（强）等效于自由群体，为表面组的解决方案提供了新的纯粹几何流体式证明。
We construct a correspondence between epimorphisms $φ\colon π_1(M) \to F_r$ from the fundamental group of a compact manifold $M$ onto the free group of rank $r$, and systems of $r$ framed non-separating hypersurfaces in $M$, which induces a bijection onto framed cobordism classes of such systems. In consequence, for closed manifolds any such $φ$ can be represented by the Reeb epimorphism of a Morse function $f\colon M \to \mathbb{R}$, i.e. by the epimorphism induced by the quotient map $M \to \mathcal{R}(f)$ onto the Reeb graph of $f$. Applying this construction we discuss the problem of classification up to (strong) equivalence of epimorphisms onto free groups, providing a new purely geometrical-topological proof of the solution of this problem for surface groups.
