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Algebraic and topological K-theory, relations with topology, commutative algebra, and operator algebras

23 votes
0 answers
584 views

What is the symmetric monoidal functor from Clifford algebras to invertible K-module spectra?

There ought to be a symmetric monoidal functor from the symmetric monoidal $2$-groupoid whose objects are Morita-invertible real superalgebras (precisely the Clifford algebras), morphisms are invertib …
Qiaochu Yuan's user avatar
18 votes
0 answers
875 views

What is operator tmf?

One of the many wonderful things about K-theory, relative to other generalized cohomology theories, is that it can be defined for not-necessarily-commutative C*-algebras. The resulting construction, i …
Qiaochu Yuan's user avatar
33 votes
2 answers
2k views

What are the "correct" conventions for defining Clifford algebras?

I have three related questions about conventions for defining Clifford algebras. 1) Let $(V, q)$ be a quadratic vector space. Should the Clifford algebra $\text{Cliff}(V, q)$ have defining relati …
Qiaochu Yuan's user avatar