Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userChern classes and generators
116
0
0.0
(
0
)
Authors
Masaki Kameko
Ask ChatGPT about the research
No Arabic abstract
We give a simple proof for the fact that algebra generators of the mod 2 cohomology of classifying spaces of exceptional Lie groups are given by Chern classes and Stiefel-Whitney classes of certain representations.
rate research
Read More
We show the non-triviality of the mod 3 Chern class of degree 324 of the adjoint representation of the exceptional Lie group E_8.
Principal circle bundle over a PL polyhedron can be triangulated and thus obtains combinatorics. The triangulation is assembled from triangulated circle bundles over simplices. To every triangulated circle bundle over a simplex we associate a necklace (in combinatorial sense). We express rational local formulas for all powers of first Chern class in the terms of mathematical expectations of parities of the associated necklaces. This rational parity is a combinatorial isomorphism invariant of triangulated circle bundle over simplex, measuring mixing by triangulation of the circular graphs over vertices of the simplex. The goal of this note is to sketch the logic of deduction these formulas from Kontsevitchs cyclic invariant connection form on metric polygons.
We construct a map from $d|1$-dimensional Euclidean field theories to complexified K-theory when $d=1$ and complex analytic elliptic cohomology when $d=2$. This provides further evidence for the Stolz--Teichner program, while also identifying candidate geometric models for Chern characters within their framework. The construction arises as a higher-dimensional and parameterized generalization of Fei Hans realization of the Chern character in K-theory as dimensional reduction for $1|1$-dimensional Euclidean field theories. In the elliptic case, the main new feature is a subtle interplay between the geometry of the super moduli space of $2|1$-dimensional tori and the derived geometry of complex analytic elliptic cohomology. As a corollary, we obtain an entirely geometric proof that partition functions of $mathcal{N}=(0,1)$ supersymmetric quantum field theories are weak modular forms, following a suggestion of Stolz and Teichner.
Let $G$ be a Lie group and $GtoAut(G)$ be the canonical group homomorphism induced by the adjoint action of a group on itself. We give an explicit description of a 1-1 correspondence between Morita equivalence classes of, on the one hand, principal 2-group $[GtoAut(G)]$-bundles over Lie groupoids and, on the other hand, $G$-extensions of Lie groupoids (i.e. between principal $[GtoAut(G)]$-bundles over differentiable stacks and $G$-gerbes over differentiable stacks). This approach also allows us to identify $G$-bound gerbes and $[Z(G)to 1]$-group bundles over differentiable stacks, where $Z(G)$ is the center of $G$. We also introduce universal characteristic classes for 2-group bundles. For groupoid central $G$-extensions, we introduce Dixmier--Douady classes that can be computed from connection-type data generalizing the ones for bundle gerbes. We prove that these classes coincide with universal characteristic classes. As a corollary, we obtain further that Dixmier--Douady classes are integral.
We show that under some assumptions on the monodromy group some combinations of higher Chern classes of flat vector bundles are torsion in the Chow group. Similar results hold for flat vector bundles that deform to such flat vector bundles (also in case of quasi-projective varieties). The results are motivated by Blochs conjecture on Chern classes of flat vector bundles on smooth complex projective varities but in some cases they give a more precise information. We also study Higgs version of Blochs conjecture and analogous problems in the positive characteristic case.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
