安德烈斯·弗洛尔

安德烈斯·弗洛尔（Andreas Floer，1956年8月23日－1991年5月15日)，德国数学家，为几何学、拓扑学以及数学物理等领域作出很可贵的开创性贡献，并提出弗洛尔同调理论（Floer homology），一种非常实用的数学工具。

## 生平

1982年波鸿鲁尔大学数学系硕士，赴美国柏克莱加州大学深造，在Clifford Taubes 教授之指导下攻读博士学位，研究范围为“monopoles on 3-manifolds”，只因必须回德服社会役，故未完成此学业，后来于1984年在波鸿Eduard Zehnder 教授之指导下获得博士学位。

弗洛尔首次的关键贡献，是解决若干关于弗拉基米尔·阿诺尔德 conjecture 与symplectomorphism 的问题。对阿诺尔德数学之研究和自己所提出的同调理论（instanton homology）之成果，使弗洛尔深得世人之肯定，并于1990年八月赴京都国际数学家大会发表演说。弗洛尔于1989年领取Sloan Fellowship 奖学金。

在1988年任柏克莱加州大学助理教授，于1990年晋升为数学系正教授。从1990年起任波鸿鲁尔大学数学教授，直到突然于1991年出人意料地自尽为止。

## 评价

"Andreas Floer's life was tragically interrupted, but his mathematical visions and striking contributions have provided powerful methods which are being applied to problems which seemed to be intractable only a few years ago." （安德烈斯·弗洛尔的生活虽然很不幸地终止，但是他对数学之远见与卓越贡献，提供了一些极为有效的方法，可以解决我们几年前还以为无法解决的问题。）

Simon Donaldson: "The concept of Floer homology is one of the most striking developments in differential geometry over the past 20 years. ... The ideas have led to great advances in the areas of low-dimensional topology and symplectic geometry and are intimately related to developments in Quantum Field Theory" ... "the full richness of Floer's theory is only beginning to be explored".（弗洛尔的同调理论是这二十年以来微分几何上最令人注目的发现之一……他的创见在几何拓扑学与辛拓扑领域造成很大的进步，并与量子场论有甚密切的关系。）……（我们目前才开始了解弗洛尔理论的整个价值。）

"Since its introduction by Andreas Floer in the late nineteen eighties, Floer theory has had a tremendous influence on many branches of mathematics including geometry, topology and dynamical systems. The development of new Floer theoretic tools continues at a remarkable pace and underlies many of the recent breakthroughs in these diverse fields."（自从安德烈斯·弗洛尔于1980年代末提出弗洛尔理论，其对数学许多分支之影响很大，包括几何、拓扑学以及动力系统。以弗洛尔理论为基础的新方法以很快的速度继续产生，不少最近的突破都是从它而出发的。）

## 重要著作

- Floer, Andreas. An instanton-invariant for 3-manifolds. Comm. Math. Phys. 118 (1988), no. 2, 215–240. Project Euclid
- Floer, Andreas. Morse theory for Lagrangian intersections. J. Differential Geom. 28 (1988), no. 3, 513–547.
- Floer, Andreas. Cuplength estimates on Lagrangian intersections. Comm. Pure Appl. Math. 42 (1989), no. 4, 335–356.

## 参考文献

- Simon Donaldson, On the work of Andreas Floer, Jahresber. Deutsch. Math.-Verein. 95 (3) (1993) , 103-120.
- The Floer Memorial Volume (H. Hofer, C. Taubes, A. Weinstein, and E. Zehnder, eds.), Progress in Mathematics, vol. 133, Birkhauser Verlag, 1995.
- Simon Donaldson, Floer Homology Groups in Yang-Mills Theory, With the assistance of M. Furuta and D. Kotschick. Cambridge Tracts in Mathematics, 147. Cambridge University Press, Cambridge, 2002. viii+236 pp. ISBN 0-521-80803-0

## 身后发表的著作

- Hofer, Helmut. Coherent orientation for periodic orbit problems in symplectic geometry (jointly with A. Floer) Math. Zeit. 212, 13–38, 1993.
- Hofer, Helmut. Symplectic homology I: Open sets in C^n (jointly with A. Floer) Math. Zeit. 215, 37–88, 1994.
- Hofer, Helmut. Applications of symplectic homology I (jointly with A. Floer and K. Wysocki) Math. Zeit. 217, 577–606, 1994.
- Hofer, Helmut. Symplectic homology II: A General Construction (jointly with K. Cieliebak and A. Floer) Math. Zeit. 218, 103–122, 1995.
- Hofer, Helmut. Transversality results in the elliptic Morse theory of the action functional (jointly with A. Floer and D. Salamon) Duke Mathematical Journal, Vol. 80 No. 1 , 251–292, 1995. Download from H. Hofer's homepage at NYU
- Hofer, Helmut. Applications of symplectic homology II (jointly with K. Cieliebak, A. Floer and K. Wysocki) Math. Zeit. 223, 27–45, 1996.

## 外部链接

- The In Memoriam website of the Department of Mathematics at the University of California, Berkeley
- The In Memoriam website of the University of California, Berkeley
- Elaborate obituary by Addison/Casson/Weinstein at OAC, Online Archive of California, 1992
- 照片看 Wikimedia Commons Category:Andreas Floer 与 a public Andreas Floer photo album on Facebook