"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." [1]（安德烈斯·弗洛爾的生活雖然很不幸地終止，但是他對數學之遠見與卓越貢獻，提供了一些極為有效的方法，可以解決我們幾年前還以為無法解決的問題。）
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"[2] ... "the full richness of Floer's theory is only beginning to be explored".[3]（弗洛爾的同調理論是這二十年以來微分幾何上最令人注目的發現之一……他的創見在幾何拓撲學與辛拓撲領域造成很大的進步，並與量子場論有甚密切的關係。）……（我們目前才開始了解弗洛爾理論的整個價值。）
"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."[4]（自從安德烈斯·弗洛爾於1980年代末提出弗洛爾理論，其對數學許多分支之影響很大，包括幾何、拓撲學以及動力系統。以弗洛爾理論為基礎的新方法以很快的速度繼續產生，不少最近的突破都是從它而出發的。）
重要著作编辑
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.
參考文獻编辑
Simon Donaldson, On the work of Andreas Floer, Jahresber. Deutsch. Math.-Verein. 95 (3) (1993) （页面存档备份，存于互联网档案馆）, 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
身後發表的著作编辑
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 （页面存档备份，存于互联网档案馆）
Hofer, Helmut. Applications of symplectic homology II (jointly with K. Cieliebak, A. Floer and K. Wysocki) Math. Zeit. 223, 27–45, 1996.
註釋编辑
^ Hofer, Weinstein, and Zehnder, Andreas Floer: 1956-1991, Notices Amer. Math. Soc. 38 (8) , 910-911
^ 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 (The above citation is from the front flap.) （页面存档备份，存于互联网档案馆）
^Mathematics: frontiers and perspectives. Edited by V. Arnold, M. Atiyah, P. Lax and B. Mazur. American Mathematical Society, Providence, RI, 2000. xii+459 pp. ISBN 0-8218-2070-2 (Amazon search)
^ From the Press Release to the Workshop New Applications and Generalizations of Floer Theory of the Banff International Research Station (BIRS), May 2007 ([5])
外部連結编辑
約翰·J·奧康納; 埃德蒙·F·羅伯遜（英语：Edmund F. Robertson）, Floer, MacTutor数学史档案（英语）
The In Memoriam website of the Department of Mathematics at the University of California, Berkeley （页面存档备份，存于互联网档案馆）
Elaborate obituary by Addison/Casson/Weinstein at OAC, Online Archive of California, 1992
照片看Wikimedia Commons Category:Andreas Floer （页面存档备份，存于互联网档案馆） 與 a public Andreas Floer photo album on Facebook
十月 05, 2023
安德烈斯, 弗洛爾, andreas, floer, 1956年8月23日, 1991年5月15日, 德國數學家, 為幾何學, 拓撲學以及數學物理等領域作出很可貴的開創性貢獻, 並提出弗洛爾同調理論, floer, homology, 一種非常實用的數學工具, 年齡19歲的弗洛爾, 目录, 生平, 評價, 重要著作, 參考文獻, 身後發表的著作, 註釋, 外部連結生平, 编辑1982年波鴻魯爾大學數學系碩士, 赴美國柏克萊加州大學深造, 在clifford, taubes, 教授之指導下攻讀博士學位, 研究範圍為,. 安德烈斯 弗洛爾 Andreas Floer 1956年8月23日 1991年5月15日 德國數學家 為幾何學 拓撲學以及數學物理等領域作出很可貴的開創性貢獻 並提出弗洛爾同調理論 Floer homology 一種非常實用的數學工具 年齡19歲的弗洛爾 目录 1 生平 2 評價 3 重要著作 4 參考文獻 5 身後發表的著作 6 註釋 7 外部連結生平 编辑1982年波鴻魯爾大學數學系碩士 赴美國柏克萊加州大學深造 在Clifford Taubes 教授之指導下攻讀博士學位 研究範圍為 monopoles on 3 manifolds 只因必須回德服社會役 故未完成此學業 後來於1984年在波鴻Eduard Zehnder 教授之指導下獲得博士學位 弗洛爾首次的關鍵貢獻 是解決若干關於弗拉基米爾 阿諾爾德 conjecture 與symplectomorphism 的問題 對阿諾爾德數學之研究和自己所提出的同調理論 instanton homology 之成果 使弗洛爾深得世人之肯定 並於1990年八月赴京都國際數學家大會發表演說 弗洛爾於1989年領取Sloan Fellowship 獎學金 在1988年任柏克萊加州大學助理教授 於1990年晉升為數學系正教授 從1990年起任波鴻魯爾大學數學教授 直到突然於1991年出人意料地自盡為止 評價 编辑 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 1 安德烈斯 弗洛爾的生活雖然很不幸地終止 但是他對數學之遠見與卓越貢獻 提供了一些極為有效的方法 可以解決我們幾年前還以為無法解決的問題 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 2 the full richness of Floer s theory is only beginning to be explored 3 弗洛爾的同調理論是這二十年以來微分幾何上最令人注目的發現之一 他的創見在幾何拓撲學與辛拓撲領域造成很大的進步 並與量子場論有甚密切的關係 我們目前才開始了解弗洛爾理論的整個價值 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 4 自從安德烈斯 弗洛爾於1980年代末提出弗洛爾理論 其對數學許多分支之影響很大 包括幾何 拓撲學以及動力系統 以弗洛爾理論為基礎的新方法以很快的速度繼續產生 不少最近的突破都是從它而出發的 重要著作 编辑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 參考文獻 编辑Simon Donaldson On the work of Andreas Floer Jahresber Deutsch Math Verein 95 3 1993 页面存档备份 存于互联网档案馆 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身後發表的著作 编辑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 页面存档备份 存于互联网档案馆 Hofer Helmut Applications of symplectic homology II jointly with K Cieliebak A Floer and K Wysocki Math Zeit 223 27 45 1996 註釋 编辑 Hofer Weinstein and Zehnder Andreas Floer 1956 1991 Notices Amer Math Soc 38 8 910 911 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 The above citation is from the front flap 页面存档备份 存于互联网档案馆 Mathematics frontiers and perspectives Edited by V Arnold M Atiyah P Lax and B Mazur American Mathematical Society Providence RI 2000 xii 459 pp ISBN 0 8218 2070 2 Amazon search From the Press Release to the Workshop New Applications and Generalizations of Floer Theory of the Banff International Research Station BIRS May 2007 5 外部連結 编辑約翰 J 奧康納 埃德蒙 F 羅伯遜 英语 Edmund F Robertson Floer MacTutor数学史档案 英语 The In Memoriam website of the Department of Mathematics at the University of California Berkeley 页面存档备份 存于互联网档案馆 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 页面存档备份 存于互联网档案馆 與 a public Andreas Floer photo album on Facebook 取自 https zh wikipedia org w index php title 安德烈斯 弗洛爾 amp oldid 79012624, 维基百科，wiki，书籍，书籍，图书馆，
