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Try this book by Jean Gallier and Diana Xu. It is aimed at undergraduates and has a nice account of Thomassen's elementary proof of the triangulation theorem in the last appendix. Or you can refer the …

There are many excellent references. It really depends on what you are after. One of the most comprehensive references is the thesis of Olivier Penacchio: http://arxiv.org/abs/math/0307156.

The statement is easily checked to be true for very stable bundles, so when you look for a counter example you will need to look for a wobbly (i.e. stable but not very stable) bundle. Suppose that $ …

Two books that I like a lot: 1) Joseph Taylor's Several complex variables with connections to algebraic geometry and Lie groups . 2) Constantin Banica and Octavian Stanasila's "Algebraic method …

This is a very interesting class of manifolds which, to my knowledge, has not been studied in any detail. One should be able to prove interesting structure theorems for such manifolds. For instance, I …

The list of references is way too long. Here are some classical texts containing both the setup and calculations: 1) P. Deligne, Le déterminant de la cohomologie, Current Trends in Arithmetical Algeb …

I will add my vote for John Stillwell's book. It has a wealth of material to draw on, and it is gorgeously written. Take also a look at "Geometry for the liberal arts" by Dan Pedoe. It is mainly abou …