Past exam of the mathematics course of the University of Cambridge / 2018 / ii / Paper 3 / 20H / b

Table of contents
- Solution b

Solution

The wedge intersection is simply connected after taking suitable neighbourhoods, so repeated application of the Seifert-van Kampen theorem gives the free product of

n

copies of

Z

with

π_{1} (RP^{2}) ≅ C_{2} .

Thus, for any basepoint,

π_{1} (X_{n}, x_{0}) ≅ ⟨ a_{1}, \dots, a_{n}, b ∣ b^{2} = 1 ⟩ ≅ F_{n} * C_{2} .

This is the fundamental group of a wedge of circles and a real projective plane.

 Ancestors (10)

 View article source

 Discussion (0)

There are no discussions about this article yet.

 Articles by others on the same topic (0)

There are currently no matching articles.

  See all articles in the same topic Create my own version