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Homotopy theory is an important sub-field of algebraic topology. It is mainly concerned with the properties and structures of spaces which are invariant under homotopy. Chief among these are the homotopy groups of spaces, specifically those of spheres. Homotopy theory includes a broad set of ideas and techniques, such as cohomology theories, spectra and stable homotopy theory, model categories, spectral sequences, and classifying spaces.

3 votes
0 answers
84 views

Reference Request: Equivariant Symplectic bordism

Non-equivariantly, symplectic bordism has been developed extensively by Ray, Gorbunov, and specially S. Kochman in this memoir: http://dx.doi.org/10.1090/memo/0496 Yet the coefficients remai …
9 votes
1 answer
425 views

Atiyah Bott-Shapiro orientation Vs Anderson-Brown-Peterson Splitting

Are the Atiyah-Bott-Shapiro Orientation and the Anderson-Brown-Peterson Splitting compatible in any sense? The first guess is that the ABS-Orientation is related to the projections o …
3 votes
1 answer
318 views

Reduced Vs unreduced cohomology in the parametrized setting.

Can someone explain the relationship between reduced and unreduced parametrized homology theories in the parametrized setting à la May-Sigurdsson with maps to a reference space $B$?. Is it just a co …
4 votes
0 answers
127 views

Spin bordism with non free involution

Is there a comprehensive account of GEOMETRIC equivariant spin bordism groups with respect to the group $ \mathbb{Z}/2$ (instead of homotopy theoretical trough equivariant Thom Spectra) …
5 votes
Accepted

Is the classifying space of a symmetric monoidal category an infinite loop space?

You need group Completion, indeed.
Nicolas Boerger's user avatar