Después de haberse roto la cremallera, llevé la sudadera a arreglar.

Because after después de, Spanish very often uses an infinitive structure rather than a fully conjugated verb.

So:

• después de haberse roto la cremallera = after the zip had broken / after the zipper broke
• literally, after having broken itself, the zipper...

Here haberse roto is the perfect infinitive, which shows that this action happened before the action in the main clause (llevé).

A more explicit alternative would be:

• Después de que se rompió la cremallera, llevé la sudadera a arreglar.

That is also correct, but the original version is very natural and compact.

Haberse roto is the perfect infinitive of romperse.

It is made up of:

• haber = auxiliary verb
• se = reflexive/pronominal particle
• roto = past participle of romper

So:

• romperse = to break / to get broken
• haberse roto = to have broken / to have got broken

In this sentence, it refers to the zipper being already broken by the time the speaker took the sweatshirt to be repaired.

Because romperse is the natural way to say that something breaks on its own or ends up broken.

Compare:

• Rompí la cremallera. = I broke the zipper.
• Se rompió la cremallera. = The zipper broke.

In your sentence, nobody is being presented as the person who broke it. The focus is simply that the zipper broke, so Spanish uses romperse.

This is very common in Spanish with things like:

• se rompió = it broke
• se perdió = it got lost
• se cayó = it fell

When a verb is in the infinitive, Spanish often attaches pronouns to the end.

So instead of writing:

• después de se haber roto ❌

Spanish says:

• después de haberse roto ✅

That se belongs to romperse, but because the whole verbal expression is in the infinitive, it gets attached to the infinitive form haber.

This is just standard pronoun placement with infinitive structures.

Spanish often uses the definite article (el, la, los, las) where English would use a possessive like his, her, its, my.

So:

• se rompió la cremallera literally = the zipper broke
• but in natural English we understand it as the zipper of the sweatshirt broke or its zipper broke

Because the context already tells us which zipper we mean, Spanish does not need to say su cremallera.

This is a very common difference between Spanish and English.

Here a arreglar expresses purpose after a verb of movement.

So:

• llevé la sudadera a arreglar = I took the sweatshirt to get repaired / to have it repaired

The pattern is:

• llevar + object + a + infinitive

Examples:

• Llevé el coche a lavar. = I took the car to be washed.
• Llevó los zapatos a arreglar. = She took the shoes to be repaired.

This often suggests that the speaker took the item somewhere so that someone else would do the repair.

Because in this structure, the object is already stated earlier:

• llevé la sudadera a arreglar

The object of arreglar is understood to be la sudadera.

Spanish often allows this with llevar + object + a + infinitive. So the second verb does not need an extra pronoun.

You could also hear:

• La llevé a arreglar. = I took it to be repaired.

There the pronoun la already appears before llevé, and it is understood with arreglar too.

Yes, you could say:

• Después de haberse roto la cremallera, llevé la sudadera para arreglarla.

That is grammatical, but it is not quite the same in feel.

• llevar algo a arreglar is a very common, idiomatic pattern meaning to take something to be repaired
• llevar algo para arreglarlo sounds more explicitly like take something in order to repair it

So the original version is more natural in everyday Spanish for this situation.

Because the speaker is talking about a completed action in the past:

• the zipper broke
• then the speaker took the sweatshirt to be repaired

The preterite llevé presents that as a single finished event.

If you used the imperfect, such as llevaba, it would usually suggest background, repetition, or an unfinished/habitual action, which does not fit as well here.

Yes. That is a very natural alternative:

• Después de que se rompió la cremallera, llevé la sudadera a arreglar.

This version uses a full subordinate clause:

• después de que + verb

The original sentence uses the more compact infinitive structure:

• después de haberse roto...

Both are correct. The original is just a little more condensed and elegant.

Usually it means I took it somewhere to be repaired, often implying that someone else would do the fixing.

So:

• llevé la sudadera a arreglar is closer to I took the sweatshirt to get it repaired or to have it repaired
• not usually I repaired it myself

If you wanted to say you repaired it yourself, you would normally say something like:

• arreglé la sudadera
• cosí la cremallera
• reparé la cremallera

Yes, cremallera is the standard word in Spain for zip / zipper.

In other Spanish-speaking countries, you may hear other words, such as:

• cierre
• zíper
• zipper

So for Spanish from Spain, cremallera is exactly what you would expect here.