Studies on function spaces defined by the exponential topology and homotopy invariants

• Project/Area Number: 23540115
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Geometry
• Research Institution: Fukuoka University
• Principal Investigator: ODA Nobuyuki 福岡大学, 理学部, 教授 (80112283)
• Project Period (FY): 2011-04-28 – 2015-03-31
• Project Status: Completed (Fiscal Year 2014)
• Budget Amount: ¥4,810,000 (Direct Cost: ¥3,700,000、Indirect Cost: ¥1,110,000); Fiscal Year 2014: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000); Fiscal Year 2013: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000); Fiscal Year 2012: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000); Fiscal Year 2011: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
• Keywords: 幾何学 / トポロジー

Outline of Final Research Achievements

The Brown-Booth-Tillotson theory was applied to homotopy theory of function spaces of based topological spaces. Making use of the exponential function for based spaces, the theory of pairing was proved without conditions for base points. The set of homotopy classes of pair maps was defined and applications of it were obtained. Conditions were obtained for the homotopy set of cyclic elements preserving maps to be monoids or groups. The dual theory was also obtained. The set with operations was defined as a generalization of the topological space and various formulas were obtained. A generalization of the theory of maximal open sets and minimal open sets in the topological spaces was obtained.

Research Products

• [Journal Article] Maximal objects and minimal objects in the sets with operations (2015)
  • Author(s): F. Nakaoka and N. Oda
  • Journal Title: Fukuoka University Science Reports Volume: 45 Pages: 1-7
  • NAID: 110009889212
• [Journal Article] Interiors and closures in a set with an operation (2014)
  • Author(s): F. Nakaoka and N. Oda
  • Journal Title: Communications of the Korean Mathematical Society Volume: 29 Issue: 4 Pages: 555-568
  • DOI: 10.4134/ckms.2014.29.4.555
  • Peer Reviewed / Open Access / Acknowledgement Compliant
• [Journal Article] The set of cyclic-element preserving maps (2013)
  • Author(s): J.-R. Kim and N. Oda
  • Journal Title: Topology and its Applications Volume: 160 Pages: 794-805
  • Peer Reviewed
• [Journal Article] The Milnor-Stasheff filtration on spaces and generalized cyclic maps (2012)
  • Author(s): N. Iwase, M. Mimura, N. Oda and Y. S. Yoon
  • Journal Title: Canadian Mathematical Bulletin Volume: 55 Pages: 523-536
  • Peer Reviewed
• [Journal Article] Homotopical presentations and calculations of algebraic K_0-groups for rings of continuous functions (2012)
  • Author(s): H. Kihara, N. Oda
  • Journal Title: Publications of the Research Institute for Mathematical Sciences, Kyoto Univ. Volume: 48 Pages: 65-82
  • NAID: 110008904422
  • Peer Reviewed
• [Journal Article] The Milnor-Stasheff filtration on spaces and generalized cyclic maps (2012)
  • Author(s): Iwase, Norio; Mimura, Mamoru; Oda, Nobuyuki; Yoon, Yeon Soo
  • Journal Title: Canad. Math. Bull. Volume: 55 Issue: 3 Pages: 523-536
  • DOI: 10.4153/cmb-2011-130-8
  • Peer Reviewed
• [Presentation] Cocyclic elements preserving maps (2015)
  • Author(s): Jae-Ryong Kim and Nobuyuki Oda
  • Organizer: ホモトピー論における有限と無限
  • Place of Presentation: 九州大学西新プラザ
  • Year and Date: 2015-02-20
• [Presentation] Brown-Booth-Tillotson products and exponentiable spaces
  • Author(s): Nobuyuki Oda
  • Organizer: Topology Seminar
  • Place of Presentation: The Ohio State University
  • Invited