Differential Gorms and Worms

The Chern–Gauss–Bonnet Theorem via Supersymmetric Euclidean Field Theories

“…In this section we provide an explicit description of 0|δ -EFT • pol (X) through functorof-points computations in Sections 2.1 and 2.2. Similar computations are carried out by Kochan andŠevera in [KŠ04]. Then we give an algebraic characterization of when 0|δ-Euclidean field theories are concordant in Section 2.3, which may be viewed as a generalization of a piece of Stokes Theorem.…”

“…Loosely, these 0|δ-dimensional field theories are a generalization of closed differential forms. For a different generalization (that considers the full diffeomorphism group of R 0|δ ) see Kochan andŠevera in [KŠ04].…”

“…Remark 3.4. Following [KŠ04], we can show that the following is a trivializing section d 1 x 1 d 1 ξ 1 · · · d 1 x n d 1 ξ n d 2 x 1 d 2 ξ 1 · · · d 2 x n d 2 ξ n ∈ Γ(Ber(T SM(R 0|2 , U )) which is independent of the choice of coordinates, verifying that the Berezinian of SM(R 0|2 , U ) is canonically trivialized independent of the choice of connection used above. However, since the integration map from the sigma model uses the metric and connection to define a Gaussian measure, we prefer the more geometric argument above.…”

From simplicial Lie algebras and hypercrossed complexes to differential graded Lie algebras via 1-jets

“…Although we do not mention it explicitly, all constructions extend more or less straightforwardly to the case when all in involved Lie groups and Lie algebras are super. Hopefully, this is a wormless paper [15].…”

On the Van Est homomorphism for Lie groupoids

“…See Guillemin-Sternberg [27] and Abad-Crainic [2]. with differentials d ′ , d ′′ was introduced by Kochan-Severa [31] under the name of differential gorms; it was subsequently studied by Vinogradov-Vitagliano [48] under the name of iterated differential forms. (Obviously, there are generalizations to n-differential algebras Ω [n] (M ).)…”