# Pseudo-Anosov Matrices of surfaces (reference request)

Can the the monodromy matrix of the action of a pseudo-Anosov homeomorphism of a surface on it's homology be of the form of a reducible or block matrix? Any such reference can be helpful. Thanks.

• "some space" is a bit unprecise... – YCor Jun 8 '17 at 10:43
• Sorry. I meant "can it be possible"? Apologies again. – diptocal47 Jun 8 '17 at 18:28
• I was asking about the meaning of space: vector space, topological space, etc, especially because "surface" appears in the title and not in the question. – YCor Jun 8 '17 at 21:18
• Yes, I meant surfaces. Sorry for the lame writing. – diptocal47 Jun 9 '17 at 6:53
• The question needs rewriting to make much sense. Let's assume the previous suggested correction: "surface" instead of "space". A surface does not have a "pseudo-Anosov monodromy matrix", but perhaps a homeomorphism of a surface does; should your question be "can the monodromy matrix of a pseudo-Anosov homemorphism of some surface be..."? If so, then what do you mean by "the monodromy matrix of a homeomorphism of a surface"? Do you mean the monodromy matrix of the action of that homeomorphism on the homology of the surface (as assumed in the answer of @IgorRivin)? – Lee Mosher Jul 8 '17 at 13:51