Images and animations

General facts on surfaces

The meridian of a torus and its core commute

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Clasification of surfaces

The torus obtained by identifying the sides of a square

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The torus with a hole is homeomorphic to two cylinders glued along a square

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Another way to represent the torus with a hole.

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Two moebius strips, glued along their boundary, form a Klein bottle.

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The genus 2 surface obtained by gluing the sides of an octogon.

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The klein bottle minus a disk.

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The connected sum of the torus and a moebius strip coincides with the sum of a klein bottle and a moebius strip.

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Cutting a Moebius srtip along a circle that does not separate, we get an orientable surface (a cylinder)

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Surgeries in a torus

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A cycle in a chain of connected sum of tori, is itself a torus.

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Relating embeddings

An isotopy between two apparently differen embeddings of the genus 2 surface in the space.

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And also in the complement of the trivial knot

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Knots and links

The trefoil knot as a torus knot.

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The figure eight knot is its own mirror image.

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