On the stable Conley index in Hilbert spaces

详细信息    查看全文

• 作者：Tirasan Khandhawit
• 关键词：37B30 ; Conley index in Hilbert spaces ; Conley index ; finite ; dimensional approximation
• 刊名：Journal of Fixed Point Theory and Applications
• 出版年：2015
• 出版时间：December 2015
• 年：2015
• 卷：17
• 期：4
• 页码：753-773
• 全文大小：805 KB
• 参考文献：1.C. Conley, Isolated Invariant Sets and the Morse Index. CBMS Reg. Conf. Ser. Math. 38, American Mathematical Society, Providence, RI, 1978.
  2.C. L. Douglas, Twisted parametrized stable homotopy theory. Preprint, arXiv:?math/-508070 , 2005.
  3.A. Floer, A refinement of the Conley index and an application to the stability of hyperbolic invariant sets. Ergodic Theory Dynam. Systems 7 (1987), 93-103.
  4.K. G?ba, M. Izydorek and A. Pruszko, The Conley index in Hilbert spaces and its applications. Studia Math. 134 (1999), 217-33.
  5.T. Khandhawit, Twisted Manolescu-Floer spectra for Seiberg-Witten. Ph.D. thesis, Massachusetts Institute of Technology, 2013.
  6.P. Kronheimer and C. Manolescu, Periodic Floer pro-spectra from the Seiberg-Witten equations. Preprint, arXiv:?math/-203243 , 2002.
  7.C. Manolescu, Seiberg-Witten-Floer stable homotopy type of three-manifolds with b 1 = 0. Geom. Topol. 7 (2003), 889-32.
  8.C. Manolescu, Pin(2)-equivariant Seiberg-Witten Floer homology and the triangulation conjecture. J. Amer. Math. Soc., to appear.
  9.J. P. May, Equivariant Homotopy and Cohomology Theory. CBMS Reg. Conf. Ser. Math. 91, American Mathematical Society, Providence, RI, 1996.
  10.P. H. Rabinowitz, Minimax methods in critical point theory with applications to differential equations. CBMS Reg. Conf. Ser. Math. 65, American Mathematical Society, Providence, RI, 1986.
  11.Rybakowski K. P.: On the homotopy index for infinite-dimensional semiflows. Trans. Amer. Math. Soc. 269, 351-82 (1982)MATH MathSciNet CrossRef
  12.Salamon D.: Connected simple systems and the Conley index of isolated invariant sets. Trans. Amer. Math. Soc 291, 1-1 (1985)MATH MathSciNet CrossRef
  13.C. Troestler and M. Willem, Nontrivial solution of a semilinear Schr?dinger equation. Comm. Partial Differential Equations 21 (1996), 1431-449.
  
• 作者单位：Tirasan Khandhawit (1)
  
  1. Kavli Institute for the Physics and Mathematics of the Universe (WPI), The University of Tokyo Institutes for Advanced Study, The University of Tokyo, 5-1-5 Kashiwa-No-Ha, Kashiwa, Chiba, 277-8583, Japan
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  Analysis
  Mathematical Methods in Physics
  
• 出版者：Birkh盲user Basel
• ISSN：1661-7746

文摘

In this paper, we study Conley theory of flows on a Hilbert space. Our approach is to apply finite-dimensional approximation which is a slight refinement of the construction developed by G?ba, Izydorek, and Pruszko (1999). For instance, we include subspaces other than invariant subspaces in the construction. As a main result, we define a stable Conley index as an object in the stable homotopy category and show that it does not depend on choices in the construction. Keywords Conley index in Hilbert spaces Conley index finite-dimensional approximation