The first text to look at is Genesis 1:28-29, where God gives man a job to do, to procreate, and to extend God's rule as God's vice regent. He was given plant life for his food. The second text is Genesis 2:15-20. There we see man at his work, specifically tilling the ground and ruling the animals by naming them. The picture portrayed between man and his environment is positive and he is working towards its benefit. All of this is necessary background to keep in mind when we look at the curse (the text of Genesis 3:12-24 is below).
12 The man said, “The woman you put here with me—she gave me some fruit from the tree, and I ate it.” 13 Then the LORD God said to the woman, “What is this you have done?” The woman said, “The serpent deceived me, and I ate.” 14 So the LORD God said to the serpent, “Because you have done this,
“Cursed are you above all livestock
and all wild animals!
You will crawl on your belly
and you will eat dust
all the days of your life.
15 And I will put enmity
between you and the woman,
and between your offspring and hers;
he will crush your head,
and you will strike his heel.”
16 To the woman he said,
“I will make your pains in childbearing very severe;
with painful labor you will give birth to children.
Your desire will be for your husband,
and he will rule over you.”
17 To Adam he said, “Because you listened to your wife and ate fruit from the tree about which I commanded you, ‘You must not eat from it,’
“Cursed is the ground because of you;
through painful toil you will eat food from it
all the days of your life.
18 It will produce thorns and thistles for you,
and you will eat the plants of the field.
19 By the sweat of your brow
you will eat your food
until you return to the ground,
since from it you were taken;
for dust you are
and to dust you will return.”
20 Adam named his wife Eve, because she would become the mother of all the living.
21 The LORD God made garments of skin for Adam and his wife and clothed them. 22 And the LORD God said, “The man has now become like one of us, knowing good and evil. He must not be allowed to reach out his hand and take also from the tree of life and eat, and live forever.” 23 So the LORD God banished him from the Garden of Eden to work the ground from which he had been taken. 24 After he drove the man out, he placed on the east side of the Garden of Eden cherubim and a flaming sword flashing back and forth to guard the way to the tree of life. (NIV)
At the rupture, three relationships were broken, the relationship between man and God, man and the cosmos, and man and his fellow man. The first of these is the most obvious. While not part of God's explicit curse, God does, in verse 22-24 banish Adam and Eve from the garden enacting the first exile. Adam and Eve's intimate relationship with God was shattered.
The second, broken interpersonal relationships, is clear from the text, as the relationship between Adam and Eve is fouled up. Also, the very next story is the story of Cain's murder of Abel, illustrating the case in point. The third is also clear: a frustration of Adam and Eve's relationship with their environment. The task of cultivation (their God given task) and their relationship with animals is frustrated. Additionally, the means through which they were to extend their dominion, reproduction also has been made more difficult. Thus we have frustration at every point due to broken relationships caused by sin.