Volume 19, issue 3 (2019)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 20
Issue 4, 1601–2143
Issue 3, 1073–1600
Issue 2, 531–1072
Issue 1, 1–529

Volume 19, 7 issues

Volume 18, 7 issues

Volume 17, 6 issues

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the Journal
Editorial Board
Editorial Interests
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Author Index
To Appear
Other MSP Journals
$C^*$–algebraic drawings of dendroidal sets

Snigdhayan Mahanta

Algebraic & Geometric Topology 19 (2019) 1171–1206

In recent years the theory of dendroidal sets has emerged as an important framework for higher algebra. We introduce the concept of a C–algebraic drawing of a dendroidal set. It depicts a dendroidal set as an object in the category of presheaves on C–algebras. We show that the construction is functorial and, in fact, it is the left adjoint of a Quillen adjunction between combinatorial model categories. We use this construction to produce a bridge between the two prominent paradigms of noncommutative geometry via adjunctions of presentable –categories, which is the primary motivation behind this article. As a consequence we obtain a single mechanism to construct bivariant homology theories in both paradigms. We propose a (conjectural) roadmap to harmonize algebraic and analytic (or topological) bivariant K–theory. Finally, a method to analyze graph algebras in terms of trees is sketched.

$C^*$–algebras, graph algebras, noncommutative spaces, dendroidal sets, simplicial sets, infinity operads, infinity categories
Mathematical Subject Classification 2010
Primary: 46L85, 55P48
Secondary: 18D50, 46L87, 55U10
Received: 14 January 2017
Revised: 27 June 2018
Accepted: 14 October 2018
Published: 21 May 2019
Snigdhayan Mahanta
Fakultät für Mathematik
Universität Regensburg