Spin cobordism categories in low dimensions

@article{Kitchloo2009SpinCC,
  title={Spin cobordism categories in low dimensions},
  author={N. Kitchloo and Jack Morava},
  journal={arXiv: Algebraic Topology},
  year={2009}
}
The Madsen-Tillmann spectra defined by categories of three- and four-dimensional Spin manifolds have a very rich algebraic structure, whose surface is scratched here. 

References

SHOWING 1-10 OF 32 REFERENCES
On the Classification of Topological Field Theories
This paper provides an informal sketch of a proof of the Baez-Dolan cobordism hypothesis, which provides a classification for extended topological quantum field theories.
The homotopy type of the cobordism category
The embedded cobordism category under study in this paper generalizes the category of conformal surfaces, introduced by G. Segal in [S2] in order to formalize the concept of field theories. Our mainExpand
The Toda conjecture
We study the Toda conjecture of Eguchi and Yang for the Gromov-Witten invariants of CP^1,using the bihamiltonian method of the formal calculus of variations. We also study its relationship to theExpand
The stable mapping class group of simply connected 4-manifolds
Abstract We consider mapping class groups Г(M) = π0 Diff(M fix ∂M) of smooth compact simply connected oriented 4-manifolds M bounded by a collection of 3-spheres. We show that if M contains ℂP 2 orExpand
The Definition of Conformal Field Theory
I shall propose a definition of 2-dimensional conformal field theory which I believe is equivalent to that used by physicists.
THOM COMPLEXES
Introduction THE spaces which form the title of this paper were introduced by Thorn in (16) as a tool in his study of differentiable manifolds. In addition certain special Thorn complexes have beenExpand
Complex Spin structures on 3 – manifolds
Two closely related descriptions of the set of Spin structures on an oriented 3–manifold are given in completely algebraic terms. A third such description was given by Deloup and Massuyeau [DM]. ItExpand
Topological quantum field theories
Following my plenary lecture on ICMP2000 I review my results concerning two closely related topics: topological quantum field theories and the problem of quantization of gauge theories. I start withExpand
Group representations, λ-rings and the J-homomorphism
THIS paper arose from a desire to apply the work of J. F. Adams ‘on the groups J(X)’ [2] to the case where Xis the classifying space B, of a finite group G. Since Adams’ calculations apply only to aExpand
The units of a ring spectrum and a logarithmic cohomology operation
Recall that if R is a commutative ring, then the set R× ⊂ R of invertible elements of R is naturally an abelian group under multiplication. This construction is a functor from commutative rings toExpand
...
1
2
3
4
...