What does this research mean for the field?

The natural structures associated with Ẑ-invariants of three-manifolds are organized by enlargements of Chern-Simons moduli spaces, enabling the construction of a generalized Ẑ-TQFT, the combinatorial categorification of WRT invariants, and the introduction of a new effective central charge. Novelty: ClaimNovelty.METHODOLOGICAL. Consensus alignment: ConsensusAlignment.NEUTRAL.

What question did this study set out to answer?

This thesis aims to explore the structure and implications of Ẑ-invariants in three-manifolds, connecting various mathematical fields.

June 7, 2026Open Access

TM Theories and Quantum Topology: Enlarged Moduli Spaces, Categorification, and Modularity

View Full Paper

Ask AI

Bookmark

Authors

MJMrunmay Milind Jagadale

Discussion

Member takes

Overview

Thesis explores Ẑ-invariants and their applications in topology, revealing new mathematical structures.

Key Points

This thesis aims to explore the structure and implications of Ẑ-invariants in three-manifolds, connecting various mathematical fields.
Constructed the Ẑ-TQFT using infinite-dimensional Hilbert spaces and Spinᶜ-structures.
Developed a combinatorial categorification of WRT invariants linked to graded Euler characteristics.
Analyzed quantum modularity of Ẑ-invariants with line defects and introduced an effective central charge for BPS degrees.
Constructed the Ẑ-TQFT which computes Ẑ-invariants effectively through topological quantum field theory.
Homologies derived from categorification show Ẑ as their graded Euler characteristic, computable for many three-manifolds.
Introduced ceff, a new topological invariant linked to the Chern-Simons invariant, differing in results from existing approaches.

Cite This Study

Mrunmay Milind Jagadale (2026) studied this question.

synapsesocial.com/papers/6a250b2d7def13d035e1b376 https://doi.org/10.7907/7756-7774

View Full Paper

Ask AI

Bookmark

June 7, 2026Open Access

TM Theories and Quantum Topology: Enlarged Moduli Spaces, Categorification, and Modularity

View Full Paper

Ask AI

Bookmark

Authors

MJMrunmay Milind Jagadale

Discussion

Member takes

Overview

Thesis explores Ẑ-invariants and their applications in topology, revealing new mathematical structures.

Key Points

This thesis aims to explore the structure and implications of Ẑ-invariants in three-manifolds, connecting various mathematical fields.
Constructed the Ẑ-TQFT using infinite-dimensional Hilbert spaces and Spinᶜ-structures.
Developed a combinatorial categorification of WRT invariants linked to graded Euler characteristics.
Analyzed quantum modularity of Ẑ-invariants with line defects and introduced an effective central charge for BPS degrees.
Constructed the Ẑ-TQFT which computes Ẑ-invariants effectively through topological quantum field theory.
Homologies derived from categorification show Ẑ as their graded Euler characteristic, computable for many three-manifolds.
Introduced ceff, a new topological invariant linked to the Chern-Simons invariant, differing in results from existing approaches.

Cite This Study

Mrunmay Milind Jagadale (2026) studied this question.

synapsesocial.com/papers/6a250b2d7def13d035e1b376 https://doi.org/10.7907/7756-7774

View Full Paper

Ask AI

Bookmark