| Co-Investigator(Kenkyū-buntansha) |
ADACHI Toshiaki Faculty of Technology, Nagoya Institute of Technology, Associate Professor, 工学部, 助教授 (60191855)
NATSUME Toshikazu Faculty of Technology, Nagoya Institute of Technology, Professor, 工学部, 教授 (00125890)
TOSIMURA Zen-ichi Faculty of Technology, Nagoya Institute of Technology, Professor, 工学部, 教授 (70047330)
YAMAKISHI Masakazu Faculty of Technology, Nagoya Institute of Technology, Lecturer, 工学部, 講師 (40270996)
OHYAMA Yoshiyuki Faculty of Technology, Nagoya Institute of Technology, Associate Professor, 工学部, 助教授 (80223981)
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| Research Abstract |
1 For fixed prime number p and a natural number n, a natural number d (【greater than or equal】 n) has been shown to exist, satisfying the following : Those properties of the p-cpmpletion of a finite spectrum which can be "seen"by K (0), K (1), … , K (n - 1), can be "seen"by just the higher Morava K -theories K (m), K (m + 1), … , K (m + d). This may be regarded as a partial evidence of Hopkinas' chromatic splitting conjecture.
2 Applying the philosophy of Hopkins ' chromatic splitting conjecture, which concerns the chromatic tower in the stable homotopy category, to the space-level unstable homotopy category, new concepts "sparce" and "mod q stupport" were introduced to generalize a theorem of Ravenel-Wilson-Yagita.
3 E (n)-based modified Adams-Novikov spectral sequence via injective resolutions, which compute the abelian group [X, Y] of the set of homotopy classes between E (n)-local spectra X, Y, has been shown to posses a horizontal vanishing line, which is independent of X, Y.
4 Replacing " suspension" by "join, " G-joiin Theorem, an unbased analogue of the G-Freudenthal Suspension Theorem in the equivariant homotopy theory, has been formulated and proven. This result immediately implies some Borsuk-Ulam type theorem.
5 (Mostly with M.Furuta, Y.Kametani, and H.Matsue) Applying the G-join Theorem to the Stable Homotopy Seiberg-Witten Invariants, Furuta's 10/8 Theorem concerning Spin closed 4 manifolds has been improved. Also, "adjunction inequality" has been obtained for some Spin closed 4 manifolds
6 (Mostly with M.Furuta and Y.Kametani) For any closed 4 manifold with b^+_2 【greater than or equal】 1, its sufficiently many iterated connected sum with itself has been shown to carry the trivial stable homotopy Seiberg-Witten invariants for any Spin^c structure, using the Devinatz-Hopkins-Smith nilpotency theorem.
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