Characteristic cohomotopy classes for families of 4-manifolds

DOI10.1515/FORUM.2010.027zbMath1200.57019arXiv2002.01738OpenAlexW2039253711MaRDI QIDQ3566429

Markus Szymik

Publication date: 8 June 2010

Published in: Forum Mathematicum (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2002.01738

zbMATH Keywords

classifying space\(K3\) surfaceFredholm operatorgroup actionstable homotopy theoryThom spectraBauer-Furuta invariantcomplex spin structureDirac bundlemonopole mapcharacteristic cohomotopy classmapping torus of a diffeomorphismsmooth submersionspin diffeomorphism groupuniversal characteristic class

Mathematics Subject Classification ID

Stable homotopy theory, spectra (55P42) Characteristic classes and numbers in differential topology (57R20) Applications of global analysis to structures on manifolds (57R57) Specialized structures on manifolds (spin manifolds, framed manifolds, etc.) (57R15) Fibrewise topology (55R70)

Related Items

Constraints on families of smooth 4-manifolds from Bauer-Furuta invariants, Tautological classes of definite 4-manifolds, On the Bauer–Furuta and Seiberg–Witten invariants of families of 4‐manifolds, Isotopy of the Dehn twist on \(K\,3\,\#\,K\,3\) after a single stabilization, Smoothability of $\mathbb {Z}\times \mathbb {Z}$-actions on 4-manifolds, Characteristic classes via 4-dimensional gauge theory, Rigidity of the mod 2 families Seiberg–Witten invariants and topology of families of spin 4-manifolds, Obstructions to smooth group actions on 4-manifolds from families Seiberg-Witten theory

Cites Work

• A stable cohomotopy refinement of Seiberg-Witten invariants. I
• Positive scalar curvature, diffeomorphisms and the Seiberg-Witten invariants
• The homotopy type of the unitary group of Hilbert space
• Equivariant K-theory
• The Seiberg-Witten equations and 4-manifold topology
• Equivariant Contractiblity of the General Linear Group of Hilbert Space