Moduli problems in derived noncommutative geometry.

Format:

Book

Thesis/Dissertation

Author/Creator:

Pandit, Pranav.

Contributor:

Pantev, Tony, 1963- advisor.

University of Pennsylvania.

Language:

English

Subjects (All):

Mathematics.

0405.

Penn dissertations--Mathematics.

Mathematics--Penn dissertations.

Local Subjects:

Penn dissertations--Mathematics.

Mathematics--Penn dissertations.

0405.

Physical Description:

140 pages

Contained In:

Dissertation Abstracts International 72-09B.

System Details:

Mode of access: World Wide Web.

text file

Summary:

We study moduli spaces of boundary conditions in 2D topological field theories. To a compactly generated linear infinity-category X , we associate a moduli functor MX parametrizing compact objects in X . The Barr-Beck-Lurie monadicity theorem allows us to establish the descent properties of MX , and show that MX is a derived stack. The Artin-Lurie representability criterion makes manifest the relation between finiteness conditions on X , and the geometricity of MX . If X is fully dualizable (smooth and proper), then MX is geometric, recovering a result of Toen-Vaquie from a new perspective. Properness of X does not imply geometricity in general: perfect complexes with support is a counterexample. However, if X is proper and perfect (symmetric monoidal, with "compact = dualizable"), then MX is geometric.

The final chapter studies the moduli of Noncommutative Calabi-Yau Spaces (oriented 2D-topological field theories). The Cobordism Hypothesis and Deligne's Conjecture are used to outline an approach to proving the unobstructedness of this space, and constructing a Frobenius structure on it.

Notes:

Thesis (Ph.D. in Mathematics) -- University of Pennsylvania, 2011.

Source: Dissertation Abstracts International, Volume: 72-09, Section: B, page: 5339.

Adviser: Tony Pantev.

Local Notes:

School code: 0175.

ISBN:

9781124732510

Access Restriction:

Restricted for use by site license.