Open-closed correspondence of K-theory and cobordism

8 Open - Closed String Correspondence in Open String Field Theory

We address the problem of describing different closed string backgrounds in background independent open string field theory: A shift in the closed string background corresponds to a collective excitation of open strings. As an illustration we apply the formalism to the case where the closed string background is a group manifold.

Spin Cobordism Determines Real K-theory

An open-closed cobordism category with background space

In this paper we introduce an open-closed cobordism category with maps to a background space. We identify the classifying space of this category for certain classes of background space. The key ingredient is the homology stability of mapping class groups with twisted coefficients.

Oriented Open-closed String Theory Revisited

String theory on D-brane backgrounds is open-closed string theory. Given the relevance of this fact, we give details and elaborate upon our earlier construction of oriented open-closed string field theory. In order to incorporate explicitly closed strings, the classical sector of this theory is open strings with a homotopy associative A∞ algebraic structure. We build a suitable Batalin-Vilkovis...

Cobordism Theory Using Steenrod Operations

In this paper I give new proofs of the structure theorems for the unoriented cobordism ring [12] and the complex cobordism ring [8, 131. The proofs are elementary in the sense that no mention of the Steenrod algebra or Adams spectral sequence is made. In fact, the only result from homotopy theory which is used in an essential way is the Serre finiteness theorem in order to know that the complex...