English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

The homotopy category of the bordism category    h   C  dhas as objects closed oriented    (  d  −  1  )   ‐manifolds and as morphisms diffeomorphism classes of   d  ‐dimensional bordisms. Using a new fiber sequence for bordism categories, we compute the classifying space of    h   C  dfor    d  =  1   , exhibiting it as a circle bundle overΩ   ∞  −  2CP   −  1   ∞    .  As part of our proof, we construct a quotient    C  1  red    of the cobordism category where circles are deleted. We show that this category has classifying spaceΩ   ∞  −  2CP   −  1   ∞and moreover that, if one equips these bordisms with a map to a simply connected space   X  , the resultingC  1  red    (  X  )can be thought of as a cobordism model for the topological cyclic homology    T  C  (  S  [  Ω  X  ]  )   .  In the second part of the paper, we construct an infinite loop space map    B   (  h   C  1  red   )   →  Q   (   Σ  2    CP  +  ∞   )in this model and use it to derive combinatorial formulas for rational cocycles on    h   C  1  redrepresenting the Miller–Morita–Mumford classesκ  i   ∈  H   (  B   (  h   C  1   )   ;  Q  )    .

The classifying space of the one‐dimensional bordism category and a cobordism model for TC of spaces