User Manuel Bärenz

31 votes

2 answers

2k views

A manifold is a homotopy type and _what_ extra structure?

asked Aug 16, 2017 at 17:15

17 votes

1 answer

792 views

Is there a constructive proof that in four dimensions, the PL and the smooth category are equivalent?

asked Jan 6, 2019 at 11:28

17 votes

2 answers

1k views

How are the Walker-Wang TQFT and the Crane-Yetter TQFT related?

asked Jan 22, 2015 at 14:49

14 votes

1 answer

655 views

Is there a PL, or topological, bordism hypothesis?

asked Jul 17, 2018 at 11:27

14 votes

2 answers

730 views

Is a unitary Hamiltonian TQFT the same as a unitary axiomatic TQFT?

asked Feb 4, 2017 at 11:46

13 votes

2 answers

749 views

Given a Kirby diagram of a 4-manifold, what's its homotopy 2-type?

asked Feb 9, 2017 at 13:14

13 votes

1 answer

647 views

A cohomology theory for fusion categories

asked Aug 11, 2017 at 10:12

13 votes

1 answer

500 views

Is there something like "Noncommutative geometry internal to a category"?

asked Apr 29, 2015 at 14:30

12 votes

3 answers

2k views

What is a good introduction to branching rules in representation theory?

asked Nov 14, 2013 at 15:52

12 votes

2 answers

719 views

Is "being a modular category" a universal or categorical/algebraic property?

asked Dec 29, 2013 at 15:18

12 votes

1 answer

529 views

Is there a "killing" lemma for G-crossed braided fusion categories?

asked Jan 18, 2018 at 14:39

10 votes

1 answer

456 views

Which manifolds are sensitive to the cocycle in the Dijkgraaf-Witten model?

asked Jun 22, 2017 at 10:45

10 votes

1 answer

286 views

Are there 4d state sum models, extended TQFTs or chain mail invariant that detect smooth structures?

asked Sep 23, 2021 at 7:22

10 votes

1 answer

802 views

What are Kirby diagrams of candidate exotic 4-manifolds?

asked Jan 24, 2014 at 17:46

10 votes

2 answers

603 views

What are TQFTs that are multiplicative under connected sums? Do bordisms with connected sum as monoidal product exist?

asked Aug 25, 2014 at 14:04

10 votes

0 answers

287 views

What's the relation between half-twists, star structures and bar involutions on Hopf algebras?

asked Sep 2, 2015 at 18:21

9 votes

1 answer

268 views

Is the modularisation of a unitary fusion category always unitary?

asked Dec 10, 2015 at 12:39

9 votes

1 answer

646 views

Is Turaev-Viro-Barrett-Westbury stronger than homotopy?

asked Jan 17, 2017 at 17:34

9 votes

2 answers

414 views

What is a true invariant of $G$-crossed braided fusion categories?

asked Aug 17, 2018 at 9:58

8 votes

1 answer

347 views

Is equality of formulas with floor rounding or integer division decidable?

asked Jul 22, 2019 at 15:41

8 votes

1 answer

184 views

Can I recover a crossed module by its homomorphisms?

asked Jun 30, 2017 at 13:58

8 votes

1 answer

250 views

Is Yetter's invariant multiplicative under connected sum?

asked Mar 14, 2018 at 17:22

8 votes

0 answers

685 views

What classifies involutive automorphisms on finite groups? What classifies involutions on finite based rings?

asked Sep 11, 2017 at 14:06

8 votes

0 answers

221 views

Ends and parametricity

asked Jan 30, 2017 at 18:24

8 votes

0 answers

403 views

Which Drinfeld centers are balanced monoidal, i.e. have a twist?

asked Sep 1, 2016 at 11:15

8 votes

1 answer

362 views

What's the (monoidal) image of a monoidal functor?

asked Sep 6, 2016 at 18:58

8 votes

0 answers

377 views

Is there a classification of 2d extended TQFTs with defects?

asked Apr 14, 2015 at 12:25

8 votes

1 answer

355 views

Does the notion of a "coherent state" exist in TQFTs? (ETQFTs?)

asked Mar 21, 2014 at 15:53

7 votes

0 answers

453 views

Is there a higher, "orientalish" version of geometric realisation?

asked Mar 29, 2015 at 12:33

7 votes

0 answers

206 views

What are (the motivations for Dominic Joyce's definition of) smooth functions for manifolds with corners?

asked Apr 25, 2017 at 12:36

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60 Questions

A manifold is a homotopy type and _what_ extra structure?

Is there a constructive proof that in four dimensions, the PL and the smooth category are equivalent?

How are the Walker-Wang TQFT and the Crane-Yetter TQFT related?

Is there a PL, or topological, bordism hypothesis?

Is a unitary Hamiltonian TQFT the same as a unitary axiomatic TQFT?

Given a Kirby diagram of a 4-manifold, what's its homotopy 2-type?

A cohomology theory for fusion categories

Is there something like "Noncommutative geometry internal to a category"?

What is a good introduction to branching rules in representation theory?

Is "being a modular category" a universal or categorical/algebraic property?

Is there a "killing" lemma for G-crossed braided fusion categories?

Which manifolds are sensitive to the cocycle in the Dijkgraaf-Witten model?

Are there 4d state sum models, extended TQFTs or chain mail invariant that detect smooth structures?

What are Kirby diagrams of candidate exotic 4-manifolds?

What are TQFTs that are multiplicative under connected sums? Do bordisms with connected sum as monoidal product exist?

What's the relation between half-twists, star structures and bar involutions on Hopf algebras?

Is the modularisation of a unitary fusion category always unitary?

Is Turaev-Viro-Barrett-Westbury stronger than homotopy?

What is a true invariant of $G$-crossed braided fusion categories?

Is equality of formulas with floor rounding or integer division decidable?

Can I recover a crossed module by its homomorphisms?

Is Yetter's invariant multiplicative under connected sum?

What classifies involutive automorphisms on finite groups? What classifies involutions on finite based rings?

Ends and parametricity

Which Drinfeld centers are balanced monoidal, i.e. have a twist?

What's the (monoidal) image of a monoidal functor?

Is there a classification of 2d extended TQFTs with defects?

Does the notion of a "coherent state" exist in TQFTs? (ETQFTs?)

Is there a higher, "orientalish" version of geometric realisation?

What are (the motivations for Dominic Joyce's definition of) smooth functions for manifolds with corners?