The aim of this paper is to give an overview of some of the existing homology theories for commutative (S-)algebras. We do not claim any originality; nor do we pretend to give a complete account. But the results in that field are widely spread in the literature, so for someone who does not actually work in that subject, it can be difficult to trace all the relationships between the different ho...

We classify invertible 2-dimensional framed and $r$-spin topological field theories by computing the homotopy groups $k$-invariant of corresponding bordism categories. By a recent result Kreck, Stolz Teichner first are given so called SKK groups. compute them explicitly using combinatorial model surfaces Novak, Runkel author.

homotopy groups π∗(Xλ)⊗Q for a family of topological spaces, once we know enough about their additive structure. This allows us to interpret the condition of realizing as an Ak map a multiple of a map f : S1 −→ G between two topological groups in terms of the existence of a rational Whitehead product of order k. Our main example will be when the Xλ are classifying spaces of symplectomorphism gr...

The notion of exterior space consists of a topological space together with a certain nonempty family of open subsets that is thought of as a ‘system of open neighborhoods at infinity’ while an exterior map is a continuous map which is ‘continuous at infinity’. The category of spaces and proper maps is a subcategory of the category of exterior spaces. In this paper we show that the category of e...

Strongly homotopy Lie algebras first made their appearance in a supporting role in deformation theory [11]. The philosophy that every deformation problem is directed by a differential graded Lie algebra leads, in the context of deformation theory of a differential graded algebra A, to a spectral sequence of which the E2-term is naturally a strongly homotopy Lie algebra. For a topological space ...