Bulletin of the Manifold Atlas (2011) Complex bordism*

of the Manifold Atlas ( 2011 ) Bordism

We give the basic definitions for the bordism groups of manifolds and survey some foundational results in the subject.

Arithmetic and Complex Bordism

Bordism theories are particular sorts of homology theories, built in accordance to the rule singular homology : simplices :: bordism : manifolds. Fixing a structure group G, the geometric chain complex GC∗(X ;G) of a space X is given by GCn(X ;G) =N f : M →X M a connected manifold with G-structure . The boundary maps in this complex are induced by the restriction of f to the boundary of M . Hen...

On images of continuous functions from a compact manifold to Euclidean space

The Nehari Manifold for a Class of Indefinite Weight Semilinear Elliptic Equations

Some Calculations with Milnor Hypersurfaces and an Application to Ginzburg’s Symplectic Bordism Ring

whose domain is the symplectic bordism ring of V. L. Ginzburg [2]. As Ginzburg proved σ to be injective, this establishes it to be an isomorphism, a result first proved by J. Morava [3] by a more topological argument. We also make some observations on the associated homology theory. For the benefit of topologists, we remark that the notion of manifold with symplectic structure is distinct from ...