TY - ELEC
AU - Kottke, Chris
PY - 2018
TI - A new theory of higher gerbes
LA - eng
M3 - Moving Image
AB - Complex line bundles are classified naturally up to isomorphism by degree
two integer cohomology $H^2$, and it is of interest to find geometric objects
which are similarly associated to higher degree cohomology. Gerbes (of
which there are various versions, due respectively to Giraud, Brylinski,
Hitchin and Chattergee, and Murray) provide a such theory associated to
$H^3$. Various notions of"higher gerbes" have also been defined, though these
tend to run into technicalities and complicted bookkeeping associated with
higher categories.
We propose a new geometric version of higher gerbes in the form of "multi
simplicial line bundles", a pleasantly concrete theory which avoids many of
the higher categorical difficulties, yet still captures key examples
including the string (aka loop spin) obstruction associated to $\frac{1}{2}\ p_1$ in
$H^4$. In fact, every integral cohomology class is represented by one of
these objects in the guise of a line bundle on the iterated free loop space
equipped with a "fusion product" (as defined by Stolz and Teichner and
further developed by Waldorf) for each loop factor. This is joint work in
progress with Richard Melrose.
N2 - Complex line bundles are classified naturally up to isomorphism by degree
two integer cohomology $H^2$, and it is of interest to find geometric objects
which are similarly associated to higher degree cohomology. Gerbes (of
which there are various versions, due respectively to Giraud, Brylinski,
Hitchin and Chattergee, and Murray) provide a such theory associated to
$H^3$. Various notions of"higher gerbes" have also been defined, though these
tend to run into technicalities and complicted bookkeeping associated with
higher categories.
We propose a new geometric version of higher gerbes in the form of "multi
simplicial line bundles", a pleasantly concrete theory which avoids many of
the higher categorical difficulties, yet still captures key examples
including the string (aka loop spin) obstruction associated to $\frac{1}{2}\ p_1$ in
$H^4$. In fact, every integral cohomology class is represented by one of
these objects in the guise of a line bundle on the iterated free loop space
equipped with a "fusion product" (as defined by Stolz and Teichner and
further developed by Waldorf) for each loop factor. This is joint work in
progress with Richard Melrose.
UR - https://open.library.ubc.ca/collections/48630/items/1.0372795
ER - End of Reference