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• CommentRowNumber1.
• CommentAuthorUrs
• CommentTimeNov 19th 2020

starting something

• CommentRowNumber2.
• CommentAuthorUrs
• CommentTimeNov 20th 2020
• (edited Nov 20th 2020)

• CommentRowNumber3.
• CommentAuthorUrs
• CommentTimeNov 20th 2020

• Taras Panov, A geometric view on $SU$-bordism, talk at Moscow State University 2020 (webpage, pdf)
• CommentRowNumber4.
• CommentAuthorUrs
• CommentTimeNov 20th 2020
• (edited Nov 20th 2020)

the SU-bordism ring is spanned by classes of Calabi-Yau manifolds: in particular the K3 surface in degree 4 and certain CY 3-folds and CY4-folds in degrees 6 and 8.

Will give this statement its own little entry now (Calabi-Yau manifolds in SU-bordism theory), for ease of cross-linking in the entries K3 surface and Calabi-Yau manifold

• CommentRowNumber5.
• CommentAuthorUrs
• CommentTimeNov 20th 2020

• CommentRowNumber6.
• CommentAuthorUrs
• CommentTimeNov 20th 2020

The kernel of the forgetful morphism

$\Omega^{SU}_\bullet \longrightarrow \Omega^{\mathrm{U}}_\bullet$

from the SU-bordism ring to the complex bordism ring, is pure torsion.

Every torsion element in the SU-bordism ring $\Omega^{SU}_\bullet$ has order 2.

• CommentRowNumber7.
• CommentAuthorUrs
• CommentTimeNov 20th 2020

and this one:

The torsion subgroup of the SU-bordism ring is concentrated in degrees $8k+1$ and $8k+2$, for $k \in \mathbb{N}$.

• CommentRowNumber8.
• CommentAuthorUrs
• CommentTimeJan 9th 2021

• CommentRowNumber9.
• CommentAuthorUrs
• CommentTimeFeb 18th 2021
• (edited Feb 18th 2021)

I have made explicit the corollary (here) that the image of the element $[K3]$ of $\Omega^{SU}_4$ is still non-trivial in $\Omega^{\mathrm{U}}_4$.

(This must be well-known, but I have trouble finding a reference that says it more directly. A half-sentence in Novikov 86, p. 216 (218 of 321) suggests this, without, however, really saying so, much less proving it.)

• CommentRowNumber10.
• CommentAuthorUrs
• CommentTimeFeb 18th 2021

for (the failure of) the Conner-Floyd isomorphism for $MSU \to KO$.