bio | website | math.tamu.edu/~branimir |
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location | College Station, TX | |
age | 29 | |
visits | member for | 5 years, 2 months |
seen | 6 hours ago | |
stats | profile views | 489 |
I'm a noncommutative geometer doing a postdoc at Texas A&M, having just completed my PhD at Caltech.
Aug
26 |
comment |
An extension of $K$-theory to topological $^*$-algebras
You can forget about involutions entirely, since the $K$-theory of a $C^\ast$-algebra as a $C^\ast$-algebra (i.e., in terms of projections and unitaries) is identical to its $K$-theory as a Banach algebra (i.e., in terms of idempotents and invertible matrices). |
Aug
15 |
comment |
Formula for the distance in noncommutative geometry
This certainly takes care of the problem at the base point $x$, but you're still left, in general, with non-differentiability of the distance function on the cut locus of $x$, no? |
Aug
15 |
comment |
Formula for the distance in noncommutative geometry
@NikWeaver Thank you for the correction. I had a silly idée fixe about approximating in the Lipschitz seminorm, so I just didn't see that it was enough to bound it from above. |
Aug
15 |
revised |
Formula for the distance in noncommutative geometry
Corrected major error in answer to Question 1, thanks to Nik Weaver's comment. |
Aug
15 |
awarded | Yearling |
Aug
14 |
awarded | Revival |
Aug
14 |
revised |
Formula for the distance in noncommutative geometry
deleted 472 characters in body |
Aug
14 |
comment |
Realisation of the noncommutative torus as a universal $ C^{*} $-algebra
+1 I'm very late to the party, but this is an excellent answer. |
Aug
14 |
answered | Formula for the distance in noncommutative geometry |
May
16 |
answered | Name for construction on two vector bundles |
Apr
26 |
comment |
A survey for various $K$-homology theories and their relationship
A possible first step towards this might be found in Hilsum's notion of bordism of unbounded KK-cycles---nothing to do with cobordism of bounded cycles---which has recently been developed further by Deeley--Goffeng--Mesland: arxiv.org/abs/1503.07398 |
Mar
22 |
awarded | Announcer |
Feb
27 |
awarded | Announcer |
Jan
4 |
comment |
Correspondences as generalized morphism between $C^*$-algebras
See, for instance, mathoverflow.net/questions/82871/… and similar discussions on MathOverflow and Math.SE. I suppose the point is that naive $\ast$-homomorphisms $A \to B$ aren't necessarily all that natural in the nonunital case, when seen through the guiding lens of Gelfand–Naimark. |
Jan
4 |
comment |
Correspondences as generalized morphism between $C^*$-algebras
I think that the heart of the matter here is that Gelfand–Naimark duality for locally compact Hausdorff spaces is a subtle business. One way to cut the Gordian knot is Woronowicz's approach, which identifies a continuous map $f: X \to Y$ as inducing a nondegenerate $\ast$-homomorphism $f^t : C_0(Y) \to M(C_0(X))$, where $M(C_0(X))$ denotes the multiplier algebra of $C_0(X)$; indeed, if $\phi : A \to M(B)$ is a nondegenerate $\ast$-homomorphism, so that $\phi(A)B$ is dense in $B$, then the induced bimodule ${}_A B_B$ satisfies both nondegeneracy and fullness. |
Jan
4 |
comment |
Correspondences as generalized morphism between $C^*$-algebras
I completely forgot; thanks for reminding me. There is a corresponding condition on the right, which says that $(E,E)$ should be dense in $A$; again, it holds for ${}_A A_A$ precisely because $A$ admits an approximate unit. |
Jan
3 |
comment |
Correspondences as generalized morphism between $C^*$-algebras
In particular, observe that the “trivial line bundle” ${}_A A_A$ satisfies this condition precisely because $A$ admits an approximate unit. |
Jan
3 |
comment |
Correspondences as generalized morphism between $C^*$-algebras
In the nonunital case, one often imposes the additional condition on ${}_A E_B$ that $A E$ be dense in $E$; this should take care of the issue in your edit. |
Jan
3 |
awarded | Announcer |
Jan
1 |
comment |
Commutative spectral triples
...firmly from the perspective of mathematical physics. |