31

Answers

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41

Do good math jokes exist?

20

Spaces with same homotopy and homology groups that are not homotopy equivalent?

12

finite generated group realized as fundamental group of manifolds

10

What are your favorite puzzles/toys for introducing new mathematical concepts to students?

6

Best online mathematics videos?

6

Homology of classifying space of spin group BSpin(n)

5

Euler characteristic of orbifolds

5

How and how much do the notations and diagrams influence our understanding of mathematical concepts?

5

Applications of string topology structure

4

subgroup of SU(N) with maximal manifold dimension

4

One-step problems in geometry

4

Analogue to covering space for higher homotopy groups?

3

Euler characteristic, Gauss-Bonnet, and a product formula

3

Realisability cohomological class as product or as immersed sphere

3

Magic trick based on deep mathematics

3

Rational homotopy theory of a punctured manifold

2

Euler Characteristic of a manifold with non-vanishing vector field,

2

prime ideals in C([0,1])

2

Cohomology classes annihilated by pullbacks

2

Homology of loop space

2

Why must a reducible flat SU(2)-connection over a homology sphere be trivial?

1

Which topics/problems could you show to a bright first year mathematics student?

1

bundle over a chain

1

Fibrewise homotopy-equivalence of unit sphere bundles vs isomorphism of tangent bundles

1

Homotopy groups of smooth manifolds?

1

What is known about the intersection pairing on H^{mid}?

1

What would be your suggestion of textbooks in Lie groups and Galois theory?

1

Equivariant maps inducing isomorphism in integral cohomology

1

When is there a deRham duality relation between the fundamental class and a top form.?

0

Obstruction Cocycles