A Free Frobenius Bialgebra Structure of Differential Forms

Details A Free Frobenius Bialgebra Structure of Differential Forms A Free Frobenius Bialgebra Structure of Differential Forms

2011-08-02

arxiv.org/abs/1108.0601v2

Mathematics

Algebraic Topology

Scientific paper

Let $M$ be a closed, oriented manifold. We prove that the quasi-isomorphism class of the $Frob_\infty^0$-bialgebra structure on $H^*(M)$ induced by the open TFT on $\Omega^*(M)$ is a homotopy invariant of the manifold. This is a three step process. First, we describe the $Frob_\infty^0$-bialgebra on $H^*(M)$ induced by the partial $Frob_\infty^0$-bialgebra on $\Omega^*(M)$. We then describe the $Frob_\infty^0$-bialgebra on $H^*(M)$ induced by the cyclic $C_\infty$-algebra on $H^*(M)$. Finally, we show these two $Frob_\infty^0$-bialgebras are the same. Since the cyclic $C_\infty$-algebra is a homotopy invariant, this proves our claim.

Affiliated with

Also associated with

No associations

Rating

A Free Frobenius Bialgebra Structure of Differential Forms does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with A Free Frobenius Bialgebra Structure of Differential Forms, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A Free Frobenius Bialgebra Structure of Differential Forms will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-510322