homological quantum field theory

A *homological* TQFT is a representation of the cobordism category that depends only on the homology of the hom-spaces.

In $d = 2$ this is also called a *homological* conformal field theory. The passage to homology forgets the conformal structure. The refinement of this concept from homology groups to chain complexes is called TCFT.

Write $Bord$ for any given cobordism category, regarded as a Top-enriched category. A **homological TQFT** is a symmetric monoidal Ab-enriched functor

$Z : H_\bullet(Bord) \to Ab
\,.$

- The string topology operations of a manifold are part of an HTQFT. See there for details.

For 2-dimensional cobordisms with closed boundary HCFT has been considered in

- Veronique Godin,
*Higher string topology operations*(2007)(arXiv:0711.4859)

A detailed treatment in $d = 2$ involving arbitrary sets of branes is in section 2 of

- Sander Kupers,
*String topology operations*MSc thesis (2011)

Revised on March 16, 2013 17:43:21
by Thomas Wasserman?
(163.1.130.189)