Volume 10 (2007)

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Homotopy theoretical considerations of the Bauer–Furuta stable homotopy Seiberg–Witten invariants

Mikio Furuta, Yukio Kametani, Hirofumi Matsue and Norihiko Minami

Geometry & Topology Monographs 10 (2007) 155–166

DOI: 10.2140/gtm.2007.10.155

arXiv: 0903.4462

Abstract

We show the "non-existence" results are essential for all the previous known applications of the Bauer–Furuta stable homotopy Seiberg–Witten invariants. As an example, we present a unified proof of the adjunction inequalities.

We also show that the nilpotency phenomenon explains why the Bauer–Furuta stable homotopy Seiberg–Witten invariants are not enough to prove 11/8–conjecture.

Keywords

stable homotopy theory, nilpotency theorem, equivariant homotopy theory, Borsuk–Ulam theorem, 4–manifold theory, Bauer–Furuta–Seiberg–Witten invariants

Mathematical Subject Classification

Primary: 55P91, 55P92, 57R57

Secondary: 55P42, 57M50

References
Publication

Received: 1 January 2005
Revised: 5 January 2006
Published: 29 January 2007

Authors
Mikio Furuta
Department of Mathematical Sciences
University of Tokyo
Tokyo 153-8914
Japan
Yukio Kametani
Department of Mathematics
Keio University
Yokohama 223-8522
Japan
Hirofumi Matsue
Department of Economics
Seijo University
Tokyo 157-8511
Japan
Norihiko Minami
Department of Mathematics
Nagoya Institute of Technology
Nagoya 466-8555
Japan